SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO
WAVES 1.
2.
A sour source ce moves moves away away from from stat statio iona nary ry obser observe verr with with a cert certai ain n speed speed v and the the ratio ratio of actual actual to to the apparent frequency as heard by the observer is n. If the two approach each other with the same speed v then the ratio would be 1 n 2 1 1+ 2− −1 ( 2 − n) 2 n n 1) 2) 3) *4) Two wir wires es of radii radii 'r' 'r' and and 2r are weld welded ed toget together her end end to to end. end. The The combin combinati ation on is stret stretched ched and is is kept kept under a tension T. The welded point is midway between the bridges. The ratio of the number of loops formed in the wires such that the !oint is a node when stationary vibrations are set up in the wires is 1 1 2 1 "
#.
".
2
#
#
1) 2) *3) 4) st An air air col colum umn n is is a tub tubee #2 cm cm long long clo close sed d at one one end end in 1 harmonic is in resonance with a tuning fork. The air column in another tube open at both ends of length $$ $$cm cm is in resonance with another tuning fork unde underr fund fundam ament ental al mode mode.. If thes thesee two two fork forkss are are sound sounded ed toge togeth ther er.. They They produ produce ce 1$ beat beatss in 2 seconds.Then the frequencies of forks are 1) 250Hz, 258Hz 2) 240Hz, 248Hz 3) 280 Hz, 272Hz *4) 264Hz, 256Hz A unif unifor orm m rope of mass mass 1%%gm 1%%gm and leng length th ".&m ".&m hangs hangs from from a rigid rigid supp suppor ort. t. The The time taken taken by the transverse wave formed in the rope to travel through the full length of the rope is 1) 1.5 sec *2) 1.41 sec 3) 1sec 4) 14.1 sec
ρ1
.
A pipe pipe of length length clos closed ed at at one end is is kept kept in in a chamb chamber er of gas of dens density ity
. A second pipe open at both
ρ2
ends is placed in a second chamber of gas of density . The compressibility of both the gases is equal if st frequency of 1 overtone in both the cases is equal then length of the second pipe is ( l
" 2
=
#
l 1
ρ
l2
2
ρ
1
1)
= # l 1
ρ1
"
2)
l2 =
ρ2
" #
l 1
ρ
1 ρ
*3)
l2 =
2
1 2
l 1
ρ
1 ρ
2
4)
1% C $.
A column of of ai air at at and a tunning fork fork produce " beats beats per sec when sound sound together. together. As As the temperature of the air columns is decreased the number of beats per sec tends to decrease and when the
1$% C temperature is
'% H z +.
the two produce 1beat per sec. Then the frequency of the tuning fork )
"% H z
'' H z
$% H z
*1) 2) 3) 4) ,hat ,hat speed speed should should a gala-y gala-y move move with with respec respectt to us so that that the sodi sodium um line line at wave wave length length &.% &.% nm is is observed as &.$$ nm.
# × 1% 1% km / sec 1) 208 km/sec
*2) 306 km/sec
3) 316 km/sec
4)
π x cos 1%% πt ) ÷ (
y = $ sin .
The The equ equat atio ion n of of a stat statio iona nary ry wave wave is . The wave is formed using a string of rd length 2%cm. The second and # antinodes are located at positions in 0cm.
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO
&.
1) 2.5 , 7.5 *2) 7.5 , 12.5 3) 5 , 10 4) 12.5 , 17.5 A rod rod 3 of length length 456 456 is hung from from two identic identical al wires A and 7. A block of mass mass 8 is hung hung at point point 9 of st the rod as shown in figure. The value of 4-6 so that the 1 overtone in wire A is in resonance with #rd harmonic of 7 is .
" L
" L
1#
*1)
2)
1# L
&
3)
# L
1+
"
4)
2"% Hz 2"% Hz 1%. a person person is standi standing ng betwee between n two tuning tuning forks forks each each vibrati vibrating ng at if both the forks move towards right at a speed of . m/s find the number of beats heard by b y the person 0:;##% m/s 1) 3 2) 6 *3) 8 4) 9 11. Two Two tuning forks forks A and 7 give '"' beats/s. beats/s. A resonates resonates with with a column of air 1$cm long long closed closed at one end and 7 with a column #2.cm long open at both ends. at 2+%?. If the temperature of air air
1#.
1".
2.
2&.
#%.
in one flute is increases to #1 %? the number of the beats bea ts per second will be 1) 1 *2) 2 3) 3 4) 4 A tuning fork of certain frequency produces " beats per second with a wire of length 2cm vibrating in its fundamental fundamental mode. The beat frequency decreases decreases when the length is slightly slightly shortened. shortened. If the length the length of the wire is shortened by shortened by %."cm it it produces produces no beats with the tuning fork. ,hat is the frequency of tuning fork 1) 200 Hz 2) 254 Hz *3) 250 Hz 4) 246 Hz The fundamental fundamental frequencie frequenciess of a closed pipe and an open pipe of differ different ent lengths lengths are #%% => and "%% => respectively. If they are !oined to form a longer pipe the fundamental frequency of the long pipe so formed is 1) 350 Hz 2) 50 Hz *3) 120 Hz 4) 100 Hz A closed closed organ organ pipe and an open organ organ pipe of same same length length produce 2 beats beats per sec when they they are set into into vibrations simultaneously in the fundamental mode. The length of open pipe is now halved and of closed pipe is doubled the number of beats produced will be 1) 8 *2) 7 3) 4 4) 2 The frequency frequency of a stretched stretched uniform uniform wire under under tension tension is in resonance resonance with the fundamental fundamental frequency frequency of a closed tube. If the tension in the wire is increased by < It is in resonance with the first overtone of the closed tube. The initial tension in the wire is *1) 1 N 2) 4 N 3) 8 N 4) 16 N ,aveleng ,a velengths ths of two notes notes in air are %/1+ %/1+ m and %/1+# m. @ach note produces produces " beats/s. beats/s. with with a third note of a fi-ed frequency. frequenc y. The speed of sound in air is 1) 400 m/s 2) 300 m/s 3) 280 m/s *4) 320 m/s
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO #1. In order to double the frequency of the fundamental note emitted by a stretched string the length is reduced #/"th of the original length and the tension is changed. The factor by which the tension is to be changed is 1) 3/8 2) 2/3 3) 8/9 *4) 9/4 æ 2p- ö æ 2pö ÷ y = a cos ç w t + f y1 =a1 sin ç t w 2 2 ç ÷ ç l ø l è è ø #2. The path difference between the waves and is 2p 2p l l f +p f-p f ( f ) 2 2 2p l 2p l 1) *2) 3) 4) ##. An organ pipe 1 closed at one end and vibrating in its first overtone and another pipe 2 open at both
(
(
)
)
ends and vibrating in its third overtone are in resonance with a given tuning fork. The ratio of the length of 1 to that of 2 is
#
1
1
#
2
#
1)
*2)
3)
4)
pt
#".
Two progressive waves y1;" sin "%% and y2;# sin "%" moving in the same direction superpose on each other producing beats. Then the number of beats per second and the ratio of ma-ium to minimum intensity of the resultant waves are respectively "& 1$ "& 1
#.
#$.
#+.
#.
#&.
"%.
pt
1
&
1
1) 2 an 2) 4 an 3) *4) 2 an A tuning fork produces + beats/s with a tuning fork of frequency 21 =>. nknown fork is now loaded and + beats/s are still heard. The frequency of unkown fork was 1) 241 Hz 2) 244 Hz *3) 258 Hz 4) 266 Hz A glass tube of 1.% m length is filled with water. The water can be drained out slowly at the bottom of the tube. If a vibrating tuning fork of frequency %% c/s is brought at the upper end of the tube and the velocity of sound is ##% m/s then the total number of resonances obtained will be 1) 4 *2) 3 3) 2 4) 1 The string of a sonometer is divided into two parts with the help of a wedge. The total length of the string is 1m and the two parts differ by 2mm. ,hen sounded together they produced two beats per second. The frequencies of the notes emitted by the two parts are 1) 4999 ! 497 Hz *2) 501 ! 499 Hz 3) 501 ! 503 Hz 4) N"ne
,hen a train is approaching the stationary observer the apparent frequency of the whistle observed as 1%% => while when it has passed away from the observer with same speed it is % =>. ?alculate the frequency of the whistle when the observer moves with the train 0:;##%m/s 1) 33.3 Hz 2) 50 Hz *3) 66.6 Hz 4) 75 Hz A car travelling at a speed of " km/hr towards a large wall horns a sound of frequency "%% => if the person stands behind the car such that the car receding from him approaches the wall the difference in frequencies of the two sounds one recieved directly from the car and the other reflected from the wall 0speed of sound is ## m/s *1) 35.9 Hz 2) 20 Hz 3) 70 Hz 4) 30 Hz An open organ pipe of length 5 vibrates in its fundamental mode. The pressure variation is ma-imum 1) A# #$e #%" ens *2) a# #$e m&'e "( #$e &e
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO
"1.
"2.
"#.
"".
3) A# &s#ances /4 &ns&e #$e ens 4) A# &s#ances /8 &ns&e #$e ens @nd correction in the closed pipe of resonating air column apparatus is 1 cm. If the first resonating length 1$ cm then the second resonating length is obtained at 1) 48 cm *2) 50 cm 3) 51 cm 4) 52 cm f 1 ,hen two waves of nearly equal frequencies super impose then the frequency of combined wave is f 2 ' f # '.
that of amplitude is and the beat frequency is Arrange them in an order f1 < f 2 < f # f 2 < f# < f 1 f # < f 2 < f 1 f1 < f # < f 2 1) *2) 3) 4) An open pipe 2% cm long resonates when filled with o-ygen with a given tuning fork. what is the length of an open pipe filled with hydrogen which will be in resonance with the same tuning fork) Biven(velocity of sound in o-ygen ; #2% msC1 and velocity of sound in hydrogen ; 12% msC1. *1) 80 cm 2) 40 cm 3) 20 cm 4) 60 cm An open organ pipe of length l is sounded together with another open organ pipe of length lD- in the fundamental tones. Epeed of sound in air is v. The beat frequency heard will be 0-FFl vx vx vl 2 vx 2
"l 2 ".
"$.
"+.
2l 2
2 x
2l
1) 2) *3) 4) A string oscillating at fundamental frequency under a tension of 22< produces $ beats per second with a sonometer. If the tension is 2$< again oscillating at fundamental note it produces $ beats per second with the same sonometer. ,hat is the frequency of the sonometer) 1) 256 2) 255 3) 280 *4) 186 The amplitude of a damped oscillator decreases to %.2 times its original magnitude in " sec. In another " sec it will decrease to - times it original magnitude. ,here - equals 1) 0.05 *2) 0.0625 3) 0.625 4) 0.00625 A travelling wave in a string has speed cm/s in Gve - direction its amplitude is 1% mm and wavelength
5 3 1m. At a particular time a point has displacement
mm. Hind the velocity vector of point
Y X P
−
p 20
j cm / s
• p 20
j cm / s
−
p 25
j cm / s
2p 35
j cm / s
*1 2 # " ". An open pipe resonates to a frequency 'f 1' and a closed pipe resonates to a frequency 'f 2'. If they are !oined together to form a longer tube then it will resonate to a frequency of 0
f 2 + 2 f 1
f1 + f 2
f1 + 2 f 2
1) 2) 3) *4) "&. The driver of a car moving towards a vertical wall notices that the frequency of his car6s horn changes from ""% => to "%=>. The speed of the car if that of the sound is #"m/s 2) 30 m/s 3) 45 m/s 4) 60 m/s *1) 15 m/s
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO %. 0A ( According to 5aplace the propagation of sound in air is an adiabatic process. 07 ( ressure has no effect on velocity of sound in a gas as long as temperature remains constant. 0? ( The velocity of sound in air changes by %.$1 m/s when temperature changes by 1%?. *1) A'' a+e #+e 2) A , - a+e "n' #+e 3) - a+e #+e 4) A , a+e "n' #+e 1. The length of the tube of a microscope is 1% cm. The focal lengths of the ob!ective and eye lenses are %. cm and 1.% cm. The magnifying power of the microscope is about 1) 5 2) 23 3) 166 *4) 500 2. A vehicle sounding a whistle of frequency 2$=> is moving on a straight road towards a hill with a velocity of 1% m/s. The number of beats produced per second is 0:elocity of sound ##% m/s 1) ze+" 2) 10 3) 14 *4) 16 #. A source of sound and an observer are approaching each other with the same speed which is equal to
1 1% times the speed of sound. The apparent relative change in frequency of source is 3) 18.2 ec+eases 4) 18.2 &nc+eases *1) 22.2 &nc+eases 2) 22.2 ec+eases ". A source producing sound of frequency 1+% => is approaching a stationary observer with a velocity 1+ m/s. The apparent change in the wavelength of sound heard by the observer 0speed of sound in air ; #"% m/s 2) 0.2 m 3) 0.4 m 4) 0.5 m *1) 0.1 m
& - 1%& . A radar sends a radio signal of frequency
=> towards an aircraft approaching the radar. If the
# - 1%# reflected wave shows a frequency shift of
=> the speed with which the aircraft is approaching the
# -1% radar in m/s 0velocity of radar signal is m/s 1) 150 2) 100 *3) 50 4) 25 $. A ,histle of frequency "% => rotates in a hori>ontal circle of radius 2m at an angular speed of 1 rad/sec. The highest frequency heard by a listener at rest with respect to centre of circle 0velocity of sound in air is ##% m/s 1) 509 Hz *2) 594 Hz 3) 598 Hz 4) 602 Hz +. An observer is standing %% m away from a vertical hill starting between the observer and the hill a police van sounding a siren of frequency 1%%% => moves towards the hill with a uniform speed. If the frequency of the sound heard directly from the siren is &+% =y the frequency of the sound heard after reflection from the hill 0in => is about 0velocity of sound ; ##% m/s 1) 1042 *2) 1032 3) 1022 4) 1012 th
1/ '
. A source of sound producing wavelength % cm is moving away from a stationary observer with of speed of sound. Then what is the wavelength of the sound heard by the observer. *1) 60 cm 2) 70 cm 3) 55 cm 4) 40 cm &. A car with a horn of frequency $2% => travels towards a large wall at a speed of 2% m/s. The frequency of echo of sound as heard by the driver is 0velocity of sound ; ##% m/s *1) 700 Hz 2) 660 Hz 3) 620 Hz 4) 580 Hz
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO $%. A person going away from a factory on his scooter at a speed of #$ kmph listens to the siren of the factory. If the frequency of the siren is $$% => and a wind is blowing opposite to the direction of motion of scooter at #$ kmph. The frequency heard by the person is 0velocity of sound is #"% m/s 2) 600 Hz 3) 510 Hz 4) 650 Hz *1) 640 Hz $1. An observer is moving with a velocity of % m/s from a source of sound of frequency 1%% =>. If speed of sound in air is ### m/s the observed frequency is 2) 91 Hz 3) 100 Hz 4) 149 *1) 85 Hz Hz $2. ,hen both source and listener move in the same direction with a velocity equal to half the velocity of sound the change in frequency of the sound as dected by the listener is 0frequency of sound n
*1) ze+"
2) n
n
n
2
#
3)
4)
1 $#.
An observer moves towards a stationary source of sound with a speed
th of the speed of sound. The
l wavelength and frequency of the source emitted are and f respectively. The apparent frequency and wavelength recorded by the observer are 1.2l 1.2l l %.l *1) 1.2( an 2) ( an 3) 0.8( an 4) 1.2( an $". A whistle emitting a sound of frequency ""%=> is tied to a string of 1.m length and rotated with an angular velocity of 2%rad/s in the hori>ontal plane. Then the range of frequencies heard by an observer stationed at a large distance from the whistle will be 0v;##%m/s 1) 400.0Hz #" 500.0Hz2) 403.3Hz #" 580.0Hz3) 420.0Hz #" 480.0Hz *4) 403.3Hz #" 484.0Hz $. The apparent frequency of the whistle of an engine becomes in the ratio of $( as the engine passes a stationary observer. If the velocity of sound is ##%m/s then the velocity of the engine is 1) 3m/s *2) 30m/s 3) 0.33m/s 4) 660m/s $$. Two cars are moving on two perpendicular roads towards a crossing with uniform speeds of +2km/hr and #$km/hr. If first car blows horn of freqency 2%=> then the frequency of horn heardby the driver of second car when the line !oining the cars makes angle of "% with the roads will be 1) 321Hz *2) 298Hz 3) 389 Hz 4) 200Hz $+. A source emitting a sound of freqency f is placed at large distance from an observer. The source starts moving towards the observer with a uniform acceleration 'a'. The frequency heard by the observer corresponding to the wave emitted !ust after the source starts is.. 0The speed of sound in medium is v. 2vf 2 vf 2 2vf 2 2vf 2 2vf - a
2vf + a
#vf - a
2vf - a
1) 2) 3) *4) $. A source of sound of frequency 2$=> is moving rapidly towards a wall with a velocity of m/s. If sound travels at a speed of #%m/s then number of beats per second heard by an observer between the wall and the source is 1) 7.7Hz 2) 9Hz 3) 4Hz *4) n"ne "( #$ese $&. The driver of a car approaching a vertical wall notices that the frequency of the horn of his car changes from "%%=> to "%=> after being reflected from the wall. Assuming speed of sound to be #"%m/s the speed of approach of car towards the wall is 1) 10m/s *2) 20m/s 3) 30m/s 4) 40m/s
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO +%. If the source is moving towards right wavefront of sound waves get modified to
1)
+1.
*2)
3)
4) N"ne "( #$ese
A wave y ; a sin 0wtCk- on a string meets with another wave producing a node at -;%. The equation of the unknown wave is 1 y ; a sin 0wtDk- 2 y;a cos 0k-Cwt # y;Ca cos 0k-Cwt *" y;C a sin 0k-Dwt +2. A wave represented by the given equation y;a cos 0wtDk- super impose on anther wave giving a stationary wave having node at -;% what is the other wave. 1 y;a cos 0wrDk- 2 y;a cos 0wtCk- *# y;Ca cos 0wtCk- " y;Ca sin 0wt D k- +#. The ratio of densities of nitrogen and o-ygen is 1"(1$. The temperature at which the speed of sound in nitrogen will be same as that in o-ygen at %? is #% ? "% ? $% ? 1"% ? 1 2 # *" +". A sample of o-ygen at
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO " wave length increases and frequency does not change % . A sound wave travelling along an air column of a pipe gets reflected at the open end of the pipe. ,hat is the phase difference between the incident and reflected waves at the open end ) # p 2 p p / 2 p 2 *# " 1 1.
Two waves of same frequency and intensity superimpose with each other in opposite phases then after superimposition the
2.
1 intensity increases by " times
2 intensity increases by two times
# frequency increases by " times
*" none of these
,hich two of the given transverse waves will give stationary waves when get superimposed Z 2 =a cos0 kx +wt Z1 =a cos0kx - wt 0A Z# =a cos 0 ky - wt
#.
07
0?
*1 A and 7 2 A and ? # 7 and ? " any two Assertion 0A ( The change in air pressure effect the speed of sound 9eason 09 ( The speed of sound in a gas is proportional to square root of pressure 1 7oth A and 9 are correct and 9 is correct e-planation of A 2 7oth A and 9 are correct but 9 is not correct e-planation of A. # A is True but 9 is false *" A is false but 9 is true
l = 600
0
A
". ,hat must be the velocity of star if the spectral line nm of a star shifts by %.1 towards longer wavelength from the position of the same line in terrestrial laboratory) 0Assume the shift to be due to oppler effect 1) 6 103 m/s *2) 5 103 m/s 3) 0.5 103 m/s 4) 6.25 103 m/s . Two particles of medium disturbed by the wave propagation are at -1 ; % and -2 ; 1 cm. The respective displacements 0in cm of the particles can be given by the equations y 1 ; 2 Ein # πt y 2 ; Ein 0# πt C π/. The wave velocity is 1) 16 cm/s *2) 24 cm/s 3) 12 cm/s 4) 8 cm/s 2 $. ?onsider a wave represented by y ; a ?os 0ωt G k- where symbols have their usual meanings. This wave has 1) an am'&#e a, (+eenc , an %ae'en#$ 2) an am'&#e a, (+eenc 2 , an %ae'en#$ 2 *3) an am'&#e a/2, (+eenc 2 , an %ae'en#$ /2 4) an am'&#e a/2, (+eenc 2 , an %ae'en#$ +. A man is watching two trains one leaving and the other coming in with equal speed of " m/s. If they sound their whistles each of frequency 2"% => the number of beats heard by the man 0velocity of sound in air is #2% m/s will be equal to *1) 6 2) 3 3) 0 4) 12
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO
π x Sin2%%π t 2%÷
y = %.Cos
. The equation of a stationary wave is where - is in cm and t is in s. The separation between consecutive nodes will be *1) 20 cm 2) 10 cm 3) 40 cm 4) 30 cm &. Two tuning forks A and 7 give " beats/s when sounded together. The frequency of A is #2% =>. ,hen some wa- is added to 7 and it is sounded with A " beats/s per second are again heard. The frequency of the tuning fork A will be 1) 312 Hz 2) 316 Hz *3) 324 Hz 4) 328 Hz
l &%. Two organ pipes both closed at one end have lengths and velocity of sound in air is : then the number of beats /s is
&1.
&2.
&#.
&".
&.
&$.
l + ∆l
.
V
V
V
V
"l
2l
"l
2l 2
∆l 2
∆l
1) 2) *3) 4) An organ pipe A closed at one end vibrating in its fundamental frequency and another pipe 7 open at both ends is vibrating in its second overtone are in resonance with a given tuning fork. The ratio of length of pipe A to that of 7 is 1) 1 2 2) 3 8 3) 2 3 *4) 1 6 A stretched wire of some length under a tension is vibrating with its fundamental frequency. Its length is decreased by "J and tension is increased by 21J. . 7y using any two tuning forks at a time the following beat frequencies are heard ( 1 2 # + . The possible frequencies of the other three forks are 1) 552, 553, 560 2) 557, 558, 560 3) 552, 553, 558 *4) 551, 553, 558 A wave represented by the equation y ; a ?os 0k- G ωt is superposed with another wave to form a stationary wave such that the point - ; % is a node. The equation for the other wave is 1) a Ein 0k- D ωt 2) a ?os 0k- G ωt *3) a ?os 0k- D ωt 4) a Ein 0k- G ωt The displacement vibration of string of length $% cm fi-ed at both ends are represented by π x y = "sin ÷ cos &$π t 2% nodes are located at distancesK. ?m e-cluding the ends of string *1) 20, 40 2) 15, 45 3) 15, 40 4) 20, 45 y = 2a sin kx cos ω t The stationary wave in closed organ pipe is the result of the superposition of y = a sin ( ω t − kx )
and y = − a cos ( ω t + kx ) 1)
y = a sin ( ω t − kx ) 3)
y = a cos ( ω t + kx ) 2) y = −a sin ( ω t + kx )
*4)
x% &+.
Two waves of equal amplitude and equal frequency travel in the same direction in a medium. The amplitude of the resultant wave is
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO 2 x%
x%
2 x%
1) 0 2) *3) 4) e#%een 0 an &. The speed of transverse waves in a stretched string is +%% cm/sec. If the string is 2m long the frequency with which it resonates in fundamental mode is + Hz + Hz 2 Hz "÷ 12÷ 1" Hz + 1) *2) 3) 4) &&. In an e-periment the string vibrates in " loops when % gm wt is placed in pan of weight 1gm. To make the string vibrate in $ loops the weight that has to be removed from the pan is appro-imately 1) 72 m *2) 36 m 3) 21 m 4) 29 m 1%%. The tension of a stretched string is increased by $&J in order to keep its frequency of vibration constant is length must be increased by
$&J *1) 30
2) 20
3) 69
4)
n1 1%1. A wire under a load has a frequency . ,hen the load is completely immersed in water its frequency is n2 the relative density of the material of the load is n12 n22 n1 n2 n12 − n22
n12 − n22 *1)
2)
n1 + n2 3)
n1 + n2 4)
x = %
1%2. The equation of a stationary wave in a string under tension T along -Cdirection from to 1 will be nπ x nπ x 2a cos sin wt 2a sin cos wt l l *1) 2) 1 π x sin wt 1 π x cos wt 2a sin n − ÷ 2a cos n − ÷ 2 l 2 l 3) 4) y = cos 2π t sin 2π x 1%#. A string is rigidly tied at two ends and its equation of vibration is given by then minimum length of string is 1 m 2π m 2 1) 1m *2) 3) 5m 4) 1%". The difference between frequencies of successive overtones of a sonometer wire is 1% =>. The frequency of its first overtone is 1) 150 Hz 2) 200 Hz 3) 250 Hz *4) 300 Hz T 1 1%. A sonometer wire vibrates with a frequency of %% => when the tension is and with a frequency of T 2 ( T1 − T 2 ) "%% => when the tension is . Its frequency of vibration for a tension 1) 450 *2) 300 3) 100 4) 210
is 0in =>
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO ' l ' 1%$. A sonometer wire of length
carries as block of mass 8 and density 4d6 at the other end. If the block is ρ immersed in a liquid of density the fundamental frequency decreases to a factor of 1
1
d 2 1 − ρ ÷ 1)
1 − ρ 2 d ÷ *2)
1
( ρ − d ) #
( d − ρ )
#
3) 4) 1%+. The equation of the standing wave in string clamped at both ends vibrating in its third harmonic is given y = %."sin ( %.#1" x ) cos ( $%%π t )
by where x and y are in cm and t in sec. a) $e (+eenc "( &+a#&"n &s 300 Hz ) $e 'en#$ "( #$e s#+&n &s 30 cm x = %1%cm #%cm c) $e n"es a+e '"ca#e a# 1) a, 2) a, c 3) , c *4) a, , c 2 × 1%11 N / m 2
%%% kg m −#
1%. If Loung6s modules of the material of a rod is and density is the time taken by a sound wave to travel through 2m of the rod is # ×1%−" sec 1.11× 1% −" sec " × 1%−" sec 1×1%−" sec 1) 2) *3) 4) 1%&. The tones that are separated by three octaves have a frequency ratio 1) 6 2) 3 3) 16 *4) 8 11%. If the temperature is raised by 1M from #%%M then the percentage charge in the speed of sound in the ( R = .#1 s / mol − k ) gaseous mi-ture is *1) 0.167 2) 2 3) 1 4) 0.334 111. A string of length l between two bridges of a sonometer vibrates in first overtone. The amplitude of vibration is ma-imum at l #l l l #l l N N " " 2 $ $ $ *1) 2) 3) 4) cann"# sa 112. A sonometer is set on the floor of a lift. ,hen the lift is at rest the sonometer wire vibrates with & g a = 1$ fundamental frequency 2$ =>. ,hen the lift goes up with acceleration the frequency of vibration of the same wire changes to 1) 512 Hz *2) 320 Hz 3) 256 Hz 4) 204 Hz 1.21 A% 11#. A standing wave having # nodes and 2 antinodes is formed between two atoms having a distance between then the wavelength of the standing wave is 1.21 A% 2."2 A% $.% A% #.$# A% *1) 2) 3) 4) 11". In a stationary wave along a string the strain is
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO 1) e+" a# #$e an#&n"es 2) :a&mm a# #$e an#&n"es 3) e+" a# #$e n"es *4) :a&mm a# #$e n"es y = a sin wt cos kx 11. In a stationary wave represented by amplitude of the component progressive wave is a
2a
a
2 *1)
2)
#a
3)
%$4)
%
11$. The elevation of a cloud is above the hori>on. A thunder is heard s after the observation of lighting. ##% ms −1 The speed of sound is . The vertical height of cloud form ground is Clod
$%% Horizon 1) 2826 m 2) 2682 m *3) 2286 m 4) 2068 m 11+. The ratio of speed of sound in neon to that in water vapours at any temperature 0when molecular weight 2.%2 ×1%−2 kg mol −1 1. ×1%−2 kg mol −1 of neon is and for water vapours is *1) 1.06 2) 1.60 3) 6.10 4) 15.2 11. The bulk modulus and the density of water are greater than those of air. ,ith this much of information we can say that velocity of sound in air 1) ;s 'a+e+ #$an &#s a'e &n %a#e+ 2) ;s sma''e+ #$an &#s a'e &n %a#e+ 3) ;s ea' #" &#s a'e &n %a#e+ *4) ann"# e c"ma+e %&#$ &#s a'e &n %a#e+ v = 1 cm / s 11&. A wave pulse on a string has the dimension shown in figure. The wave speed is . If point O is t = #s a free end. The shape of wave at time is v = 1cm / s 1cm ! 2cm
1cm 1cm
! 1cm !
1)
1cm 2)
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO !
1cm
2cm
1cm
!
1cm
3)
*4)
y1
= a sin kx cos ω t
12%. @quations of a stationary and a travelling waves are as follows
y2
x1
= a sin ( ω t − kx )
=
π
x2
#k
The phase difference between two points
and
and
=
#π
φ 1
2k are
φ 2 and
φ 1 φ 2 respectively for the two waves. The ratio $ 1) 1
2)
is #
$
"
+
3)
*4)
l 121. The time taken by sound waves to travel the distance if the air temperature between them varies T 1 T 2 v = α T linearly from to 0velocity of sound in air is given by 2l 2l l l
α ( T2
+
T 1 )
α ( T2
*1)
2)
−
T 1 )
α ( T2
+
3)
T 1 )
α ( T2 4)
−
T 1 )
ρ
122. A standing wave is maintained in a homogeneous string of crossCsectional area PsQ and density . It is formed by the superposition of two waves travelling in opposite directions given by the equation y1 = a sin ( ω t − kx ) y2 = 2 a sin ( ω t + kx ) and The total mechanical energy confined between the sections corresponding to the ad!acent a ntinodes is #π s ρω 2 a 2 'π s ρω 2 a 2 2π s ρω 2 a 2 π s ρω 2 a 2 2k
2k
1) 2) 12#. Two waves are represented by y1 = sin 2π ( +t − %.2 x )
2k *3)
2k 4)
y2 = 1%sin 2π ( 1'%t − %.'% x ) " 1 " 2
The intensity ratio 1( 2 1)
of the two waves is 1( " 1( 2) 3)
1(1$ *4)
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO y = " sin 2π × cos ωτ
12". The vibration of a stretched string fi-ed at both ends are described by .The minimum length of the wire will be 2π m 1) 1m *2) 0.5 m 3) 5 m 4) 12. The equation for the vibration of a string fi-ed at both ends vibrating in its third harmonic is given by
y = 2cm sin ( %.$cm−1 ) x cos
1) 24.6 cm
−1 ( %%π s ) t
2) 12.5 cm
The length of the string is 3) 20.6 cm *4) 15.7 cm 1 n
12$. A string is under tension so that its length is increased by times its original length. The ratio of fundamental frequency of longitudinal vibrations and transverse vibrations will be( n 2 (1
1( n 1)
2)
n (1
n (1
*3)
4) %% C 2'% C 12+. A tuning fork produces a wave of wavelength 11% cm in air at . The wavelength at would be 1) 110 cm *2) 115 cm 3) 120 cm 4) 130 cm 12. The speed of sound in a mi-ture of 1 mol. Of =elium and 2 mol. Of o-ygen at #%%M is 1) 300 m/s *2) 400 m/s 3) 500 m/s 4) N"ne "( #$ese 12&. A standing wave is produced on a string clamped at one end and free at the other. The length of the string λ / " λ / 2 *1) :s# e an &n#e+a' m'#&'e "( 2) :s# e an &n#e+a' m'#&'e "( λ / 2 λ 3) :s# e an &n#e+a' m'#&'e "( 4) :a e an &n#e+a' m'#&'e "(
1#%. 25 #n&n ("+ks a+e a++ane &n se+&es &n #$e "+e+ "( ec+eas&n (+eenc. An #%" sccess&e ("+ks +"ces 3 ea#s/s. ;( #$e (+eenc "( #$e (&+s# #n&n ("+k &s #$e "c#ae "( #$e 'as# ("+k, #$en #$e (+eenc "( #$e 21s# ("+k &s 1) 72 Hz 2) 288 Hz *3) 84 Hz 4) 87 Hz 1#1. A police car moving at 22m/s chases a motorcyclist. The policeman sounds his horn at 1+$=> while both of them move towards a stationary siren of frequency 1$=>.?alculate the speed of the motorcycle If it is given that the motorcyclist does not observe any beats 0:elocity of sound;##%m/s 1 ## m/s *2 22 m/s # Rero " 11 m/s 1#2. An open pipe of length 'l ' vibrates in fundamental mode. The pressure variation is ma-imum at l " 1)
(+"m ens
*2) #$e m&'e "( #$e &e l
3) #$e ens "( &e 4) a# (+"m ens "( &e 1##. Two vibrating strings of the same material but length 5 and 25 have radii 2r and r respectively. They are stretched under the same tension. 7oth the strings vibrate in their fundamental modes the one of length
f 1 5 with frequency 1) 2
f 2 and the other with frequency . The ratio 2) 4 3) 8
f1 / f 2 is given by *4) 1
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO π ( y t ) = %.%2 cos '%π t + ÷ cos ( 1%π x )
2
1#". A wave disturbance in a medium is described by where - and y are in meter and t is in second Then wrong statement is x = %.# m x = %.1' m 1) A n"e "cc+s a# 2) an an#&n"e "cc+s a# ' ms−1 3) $e see "( %ae &s *4) $e %ae'en#$ "( %ae &s 0.3 m x 1#. The e-tension in a string obeying =ooke6s law is . The speed of transverse wave in the stretched string is v. if the e-tension in the string is increased to 1.- the speed of wave will be 1.'% v %.+'v %.$1v *1) 1.22 2) 3) 4) 2 y = a cos ( 2π nt − 2π x / λ ) 1#$. The equation
represents a wave with(
λ 1) am'&#e a, (+eenc n an %ae'en#$
λ 2) am'&#e a, (+eenc 2n an %ae'en#$ 2
λ 3) am'&#e a/2, (+eenc 2n an %ae'en#$
λ *4) am'&#e a/2, (+eenc 2 n an %ae'en#$
/2
1#+. The figure shows four progressive waves A 7 ? N . It can be concluded from the figure that with respect to wave A(
π / 2 N
π / 2
1) $e %ae &s a$ea a $ase an'e "(
#$e %ae - 'as e$&n a $ase an'e π / 2 N *2) $e %ae &s 'as e$&n a $ase an'e "( #$e %ae - &s a$ea a $ase an'e π / 2
π N 3) $e %ae &s a$ea a $ase an'e "(
π
#$e %ae - 'as e$&n a $ase an'e . π N π 4) $e %ae &s 'as e$&n a $ase an'e "( #$e %ae - 'as e$&n a $ase an'e .
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO 1#. ,hat is the percentage change in the tension necessary in a sonometer of fi-ed length to produce a note one octave lower 0half of original frequency th an before 1) 25 2) 50 3) 67 *4) 75 1#&. A chord attached about an end to a vibrating fork divides it into $ loops when its tension is #$ <. The tension at which it will vibrate in " loops is( 2" N #$ N $" N 1) 2) 3) *4) 81 N 1"%. Two vibrating strings of same length same cross section area and stretched to same tension are made of v1 ρ N 2 ρ materials with densities . @ach string is fi-ed at both ends. If represents the frequency of v1 / v2 v2 ρ fundamental mode of vibration of the one made with density and for another then is 1 1 2
2
2
1) 2) 2 *3) 4) 1"1. A string of length 5 is clamped at each end and vibrates in a standing wave pattern. The wavelengths of constituent traveling waves can not be *1) 3 2) 2 3) 2/3 4) /2
1"2. A mass less rod of length 5 is suspended by two identical strings A7 and ? of equal length. A block of mass m is suspended from point O such that 7O is equal to 4-6. Hurther it is observed that the frequency of 1st harmonic in A7 is equal to 2nd harmonic frequency in ?. 4-6 is
L
" L
# L
L
'
"
"
*1)
2)
3)
ρ
4)
1"#. An ob!ect of specific gravity is hung from a thin steel wire. The fundamental frequency for transverse standing waves in the wire is #%% =>. The ob!ect is immersed in water so that one half of its volume is submerged. The new fundamental frequency in => is.
2 ρ − 1 #%% ÷ 2 ρ
*1)
1/ 2
2 ρ #%% ÷ 2 ρ − 1 2)
1/ 2
2 ρ ÷ 2 ρ − 1
2 ρ − 1 ÷ 2 ρ
#%% 3)
#%% 4)
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO x = L 1"". The ends of stretched wire of length 5 are fi-ed at - ; % and In one e-periment the displacement y1 = A sin ( π x / L) sin ω t # 1 of the wire is and energy is and in another e-periment its displacement is y2 = A sin ( 2π x / L ) sin2ω t # 2 . and energy is #2 = 2 # 1
then #2 = " # 1 #2 = 1$# 1 #2 = # 1 1) 2) *3) 4) 1". A stretched wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of & kg is suspended from the wire. ,hen this mass is replaced by a mass 8 the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of 8 is *1 ) 25 k 2) 5 k 3) 12.5 k 4) 1/25 k y1 = a sin kx cos ω t 1"$. @quation of a stationary and a traveling waves are as a follows and y1 = a sin0ω t − kx . π #π
=
#k
=
2k
φ 1
φ 2
The phase difference between two points S1 and -2 is in the standing wave 0y1 and is in φ 1 φ 2 travelling wave 0y2 then ratio is 1) 1 2)5/6 3)3/4 *4)6/7 1"+. A uniform rope having mass m hangs vertically from a rigid support. A transverse wave pulse is produced at the lower end. The speed u of wave pulse varies with height h from the lower end as( 1)
*3)
2)
4)
1". The mass of 1 mole of air is 2& - 1%C# kg then speed of sound in air at standard temperature and pressure is *1 ##1.# m/s 2 2% m/s # #1% m/s " #2% m/s
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO 1"&. Two sitar strings A and 7 playing the note 4ha6 are slightly out of tune and produce beats of frequency $ =>. The tension of the string 7 is slightly increased and the beat frequency is found to decrease to # =>. If frequency of A is "2 => then original frequency of 7 is 1 "#" => *2 "22 => # "2 => " "#1 => 1%. The wrong statement in the following pertaining to stationary wave 1 All the particles e-cept at nodes vibrate with different amplitude but same frequency as that of component wave p 2 The phase difference between the particles in the successive loops is . # The phase difference between any two particles in same loop is >ero *" At nodes the strain is >ero 11. A Transverse wave equation by y ;y% sin 20t/T C -/U . if ma-imum particle velocity is equal to " times the wave velocity them wave length is 1 <V/# 2 <V/" # <V/ *" <V/2 d A= a+b−c 12. The amplitude of a wave is represented by . Then resonance will occur when 1 a ; % b ; c 2 b ; % a ; c # b D a ; c *" all the above 1#. A ( A person hears ma-imum sound at displacement anti node 0or pressure node 7 ( 3uality of sound from one open organ pipe is different than from a closed pipe of same frequency ? ( Two organ pipes of same length open at both ends produce sound of different pitch if their radii are different ( If oil of density higher than water is filled in place of water in a resonance tube its frequency remain unchanged *1 All are true 2 A 7 are only true # 7? are true " A ? are only true
px 20÷
p
1". The equation of a stationary wave is y ; %.& ?os Ein02%% t where - is in cm and t is in seconds. The separation between consecutive nodes is 1 1% cm *2 2% cm # #% cm " "% cm 1. The length of a sonometer wire A7 is 1%% cm. ,here should the two bridges be placed from A to divide the wire in # segments whose fundamental frequencies are in the ratio of 1 ( 2 ( $ 1 #% cm &% cm *2 $% cm &% cm # "% cm % cm " 2% cm #% cm C# 1$. A wire whose linear density is - 1% kg/m is stretched between two points with a tension "% <. The wire resonates at a frequency of "2% =>. The ne-t higher frequency at which the same wire resonates is "&% =>. ,hat is the length of the wire) 1 1.2 m 2 1. m *# 2.1 m " .1 m 1+. The ratio of the speed of the sound in nitrogen gas to that in helium gas at #%% M is 2
1
7
7
3 5
6 5
1 2 *# " 1. A cylindrical tube open at both ends has a fundamental frequency f o in air. The tube is dipped vertically into water such that half of its length is inside water. The fundamental frequency of the air column now is
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO f o 2
3f o f o
4
f o
1 *2 # " 2 1&. An open organ pipe and closed pipe have same length. The ratio of frequencies of their nth over tone is n +1
2 ( n + 1)
n
n +1
2n + 1
2n + 1
2n + 1
2n
1
*2
p
#
p
"
1$%. Two progressive waves y1 ; " sin "%% t and y2 ; # sin "%" t moving in the same direction superpose on each other producing beats. Then the number of beats per second and the ratio of ma-imum to minimum intensity of the resultant waves are respectively 1 2 and /1 2 " and "&/1 # " and 1$/& *" 2 and "&/1 1$1. $" tuning forks are arranged such that each fork produces " beats per second with ne-t one. If the frequency of the last fork is octave of the first the frequency of 1$th fork is 1 #1$ => 2 #22 => *# #12 => " #% => 1$2. Two tuning forks A and 7 vibrating simultaneously produce beats/s. Hrequency of 7 is 12 =>. If one arm of A is filed the number of beats per second increases. Hrequency of A is 1 %2 => 2 %+ => *# 1+ => " 22 => 1$#. The equation for the vibration of a string fi-ed at both ends vibrating in its third harmonic is given by y ; p 2sin 0%.$- ?os0%% t y and - in cm. Then length of the string is 1 12. cm 2 2".$ cm *# 1.+ cm " 2%.$ cm 1$". A string is under tension so that its length is increased by 1/- times it original length. The ratio of fundamental frequency of longitudinal vibrations and transverse vibrations will be x2 : 1 x x 1 - ( 1
*2
( 1
#
" 1 (
1$. A standing wave is maintained in a homogenous string of cross sectional area A and density formed by the superposition of two waves travelling in opposite direction given by the equations
r . Its
y = 2a sin ( wt − kx ) 1 y
2
= a sin ( wt + kx )
Total mechanical energy confined between the sections corresponding to the ad!acent anti node is 2 2 2 2 5pAr w a 5pAr w a pAr w2a 2 2pAr w2a 2 2k 2k 2k 2k 2 2 # " *1 1$$. Hirst overtone frequency of a closed pipe is equal to the first overtone frequency of an open organ pipe. Hurther nth harmonic of closed organ pipe is also equal to the mth harmonic of open pipe where n and m are 1 " *2 & $ # + " + # 1$+. Hor certain organ pipe three successive resonance frequencies are observed at "2 => & => and +$ => respectively. If the speed of sound in air is #"% m/s then the length of the pipe is 1 %.2 m 2 %." m # 2 m *" 1 m
SRICHAITANYA EDUCATIONAL INSTITUTIONS _NAGOLE _CO
