Practice Test Vibrations and Waves Multiple Choice: Identify the choice that best completes the statement or answers the question. Fill in the corresponding oval on your Scantron sheet. 1.
A large spring requires requires a force of 150 N to compress it only 0.010 m. What is the spring constant of the spring? a 125 000 N/m b 15 000 N/m c 15 N/m d 1.5 N/m e 1.0 N/m
2.
Tripling Tripling the weight suspene !ertically from a coil spring will result in a change in the isplacement of the spring"s lower en #y what factor? a 0.$$ b 1.0 c $.0 d %.0 e 12
3.
A mass of 0.&0 'g( attache to a spring with a spring constant of )0 N/m( is set into simple harmonic motion. What is the magnitue of the acceleration of the mass when at its ma*imum isplacement of 0.10 m from the equili#rium position? a +ero b 5 m/s2 c 10 m/s 2 d 20 m/s 2 e 2$ m/s 2
4.
A mass of &.0 'g( resting on a hori+ontal frictionless frictionless surface( is attache on the right to a hori+ontal spring with spring constant 20 N/m an on the left to a hori+ontal spring with spring constant 50 N/m. ,f this system is mo!e from equili#rium( what is the effecti!e spring constant? a $0 N/m b -$0 N/m c 0 N/m d 1& N/m e -1& N/m
5.
uppose there is an o#ect for which F kx kx.. What will happen if the o#ect is mo!e away from equili#rium 3 x 3 x 04 an release? a ,t will return to the equili#rium position. b ,t will mo!e further away with constant !elocity. c ,t will mo!e further away with constant acceleration. d ,t will mo!e further away with increasing acceleration. e None of the a#o!e.
6.
A 0.20-'g o#ect is oscillating on a spring with a spring constant of k 15 N/m. What is the potential energy of the system when the o#ect isplacement is 0.0&0 m( e*actly half the ma*imum amplitue? a +ero b 0.00 0 6 c 0.012 6 d 2.5 6 e $.& 6
7.
A 0.20 'g o#ect( attache to a spring with spring constant k 10 N/m( is mo!ing on a hori+ontal frictionless surface in simple harmonic motion of amplitue of 0.0)0 m. What is its spee at the instant when its isplacement is 0.0&0 m? 37int8 9se conser!ation of energy.4 a %.) m/s b &.% m/s c &% cm/s d 2&.5 cm/s e 5$ cm/s
8.
A mass of 0.&0 'g( hanging from a spring with a spring constant of )0 N/m( is set into an up-an-own simple harmonic motion. What is the spee of the mass when mo!ing through the equili#rium point? The starting isplacement from equili#rium is 0.10 m. a +ero b 1.& m/s c 2.0 m/s d $.& m/s e &.2 m/s
9.
A mass of 0.&0 'g( hanging from a spring with a spring constant of )0 N/m( is set into an up-an-own simple harmonic motion. What is the spee of the mass when mo!ing through a point at 0.05 m isplacement? The starting isplacement of the mass is 0.10 m from its equili#rium position. a +ero b 1.& m/s c 1. m/s d 1.2 m/s e 1.0 m/s
10.
A 0.20-'g #loc' rests on a frictionless le!el surface an is attache to a hori+ontally aligne spring with a spring constant of &0 N/m. The #loc' is initially isplace &.0 cm from the equili#rium point an then release to set up a simple harmonic motion. What is the spee of the #loc' when it passes through the equili#rium point? a 2.1 m/s b 1. m/s c 1.1 m/s d 0.5 m/s e 0.&2 m/s
11.
A 0.20-'g #loc' rests on a frictionless le!el surface an is attache to a hori+ontally aligne spring with a spring constant of &0 N/m. The #loc' is initially isplace &.0 cm from the equili#rium point an then release to set up a simple harmonic motion. A frictional force of 0.$ N e*ists #etween the #loc' an surface. What is the spee of the #loc' when it passes through the equili#rium point after #eing release from the &.0-cm isplacement point?
a b c d e
0.&5 m/s 0.$ m/s 0.)0 m/s 1.2 m/s 1.& m/s
12.
uppose a 0.$-'g mass on a spring that has #een compresse 0.10 m has elastic potential energy of 1 6. What is the spring constant? a 10 N/m b 20 N/m c 200 N/m d $00 N/m e &00 N/m
13.
An ore car of mass & 000 'g rolls ownhill on trac's from a mine. At the en of the trac's( 10.0 m lower in ele!ation( is a spring with k &00 000 N/m. 7ow much is the spring compresse in stopping the ore car? ,gnore friction. a 0.1& m b 0.5 m c 1.&0 m d 1.% m e 2.&$ m
14.
An o#ect is attache to a spring an its frequency of oscillation is measure. Then another o#ect is connecte to the first o#ect( an the resulting mass is four times the original !alue. :y what factor is the frequency of oscillation change? a 1/& b 1/2 c 1/1 d 2 e &
15.
:y what factor must one change the weight suspene !ertically from a spring coil in orer to triple its perio of simple harmonic motion? a 1/% b 0.$$ c $.0 d %.0 e 12
16.
;or a mass suspene on a spring in the !ertical irection( the time for one complete oscillation will epen on8 a the !alue for g 3the acceleration ue to gra!ity4. b the istance the mass was originally pulle own. c the ma*imum spee of the oscillating mass. d the time oesn"t epen on any of the a#o!e. e #oth choices A an < are !ali.
17.
A car with #a shoc's #ounces up an own with a perio of 1.50 s after hitting a #ump. The car has a mass of 1 500 'g an is supporte #y four springs of force constant k . What is k for each spring? a 5)0 N/m b 5 )50 N/m c & &&0 N/m d $ $0 N/m e 2 )0 n/m
18.
A mass on a spring !i#rates in simple harmonic motion at a frequency of &.0 7+ an an amplitue of &.0 cm. ,f a timer is starte when its isplacement is a ma*imum 3hence x & cm when t 04( what is the spee of the mass when t $ s? a +ero b 0.00 5 m/s c 0.015 m/s d 0.02& m/s e 0.0&$ m/s
19.
A mass on a spring !i#rates in simple harmonic motion at a frequency of &.0 7+ an an amplitue of &.0 cm. ,f a timer is starte when its isplacement is a ma*imum 3hence x & cm when t 04( what is the acceleration magnitue when t $ s? a +ero b ).1$ m/s 2 c 1&.$ m/s 2 d 25.$ m/s 2 e $2.& m/s 2
20.
An o#ect mo!ing in simple harmonic motion has an amplitue of 0.020 m an a ma*imum acceleration of &0 m/s2. What is the frequency of the system? a 0.0 7+ b 51 7+ c .1 7+ d 1 7+ e 1) 7+
21.
The position of a 0.&-'g mass unergoing simple harmonic motion is gi!en #y x 30.10 m4 cos 3 πt/14. What is its perio of oscillation? a 100 s b $2 s c 1 s d ).0 s e &.5 s
22.
The position of a 0.&-'g mass unergoing simple harmonic motion is gi!en #y x 30.10 m4 cos 3 πt/14. What is the ma*imum net force on the mass as it oscillates? a $.% × 10-$ N b %.% × 10-$ N c 1.$ × 10-$ N d 5.& × 10-2 N
e
23.
.$ N
Tripling the mass of the #o# on a simple penulum will cause a change in the frequency of the penulum swing #y what factor? a 0.$$ b 1.0 c $.0 d %.0 e 12
24.
A simple penulum has a perio of 2.0 s. What is the penulum length? 3 g %.) m/s 24 a 0.$ m b 0.) m c 0.%% m d 2.& m e $.5 m
25.
A simple penulum of length 1.00 m has a mass of 100 g attache. ,t is rawn #ac' $0.0 ° an then release. What is the ma*imum spee of the mass? a 1.1& m/s b $.1$ m/s c 2.21 m/s d 1.2 m/s e 2.5 m/s
26.
A simple penulum has a mass of 0.25 'g an a length of 1.0 m. ,t is isplace through an angle of $0 ° an then release. After a time( the ma*imum angle of swing is only 10 °. 7ow much energy has #een lost to friction? a 0.2% 6 b 0.5 6 c 0.)0 6 d 1.0 6 e 1.2 6
27.
When car shoc' a#sor#ers wear out an lose their amping a#ility( what is the resulting oscillating #eha!ior? a unerampe b critically ampe c o!erampe d hyperampe
28.
;or a wa!e on the ocean( the amplitue is8 a the istance #etween crests. b the height ifference #etween a crest an a trough. c one half the height ifference #etween a crest an a trough. d how far the wa!e goes up on the #each. e one half the istance #etween crests.
29.
As a gust of win #lows across a fiel of grain( a wa!e can #e seen to mo!e across the fiel as the tops of the plants sway #ac' an forth. This wa!e is a8 a trans!erse wa!e. b longituinal wa!e. c polari+e wa!e. d interference of wa!es. e #oth choices : an < are !ali.
30.
The wa!elength of a tra!eling wa!e can #e calculate if one 'nows the8 a frequency. b spee an amplitue. c amplitue an frequency. d frequency an spee. e spee.
31.
A musical tone( soune on a piano( has a frequency of &10 7+ an a wa!elength in air of 0.)00 m. What is the wa!e spee? a 10 m/s b 2$5 m/s c $2) m/s d 5) m/s e $ m/s
32.
,f a raio wa!e has spee $.00 × 10) m/s an frequency %&. =7+( what is its wa!elength? a ).) m b 1.20 m c 2.50 m d $.1 m e &.21 m
33.
a b c d e
the istance 0 to A. twice the istance 0 to A. the istance x2 to x$. twice the istance x2 to x$. the istance 0 to x1.
34.
:ats can etect small o#ects such as insects that are of a si+e appro*imately that of one wa!elength. ,f #ats emit a chirp at a frequency of 0 '7+( an the spee of soun wa!es in air is $$0 m/s( what is the smallest si+e insect they can etect? a 1.5 mm b $.5 mm c 5.5 mm d .5 mm e %.5 mm
35.
Wa!es propagate at ).0 m/s along a stretche string. The en of the string is !i#rate up an own once e!ery 1.5 s. What is the wa!elength of the wa!es that tra!el along the string? a $.0 m b 12 m c .0 m d 5.$ m e 10 m
36.
A long string is pulle so that the tension in it increases #y a factor of three. ,f the change in length is negligi#le( #y what factor oes the wa!e spee change? a $.0 b 1. c 0.5) d 0.$$ e 0.21
37.
Tripling the mass per unit length of a guitar string will result in changing the wa!e spee in the string #y what factor? a 0.5) b 1.00 3i.e.( no change4 c 1.$ d $.00 e %.00
38.
A 2.0-m long piano string of mass 10 g is uner a tension of $$) N. ;in the spee with which a wa!e tra!els on this string. a 1$0 m/s b 20 m/s c 520 m/s d 1 0&0 m/s e 1 200 m/s
39.
Trans!erse wa!es tra!el with a spee of 200 m/s along a taut copper wire that has a iameter of 1.50 mm. What is the tension in the wire? 3The ensity of copper is ).%$ g/cm $.4 a 1 )%0 N b 1 20 N c $1 N d $15 N e 2& N
40.
;or a wa!e tra!eling in a string( #y what factor woul the tension nee to #e increase to ou#le the wa!e spee? a 1.& b 2.0 c &.0 d ).0 e 1
41.
The superposition principle has to o with which of the following? a effects of wa!es at great istances b the a#ility of some wa!es to mo!e !ery far c how isplacements of interacting wa!es a together d relati!istic wa!e #eha!ior e #oth choices A an < are !ali.
42.
,f a wa!e pulse is reflecte from a free #ounary( which of the following choices #est escri#es what happens to the reflecte pulse? a #ecomes in!erte b remains upright c hal!e in amplitue d ou#le in amplitue e #oth choices : an < are !ali.
43.
Two water wa!es meet at the same point( one ha!ing a isplacement a#o!e equili#rium of 0 cm an the other ha!ing a isplacement a#o!e equili#rium of )0 cm. At this moment( what is the resulting isplacement a#o!e equili#rium? a 1&0 cm b 100 cm c 0 cm d 50 cm e ,nformation a#out the amplitues neee to #e gi!en to fin an answer.
44.
The wor' one to mo!e a spring away from its equili#rium position is equal to a c the ratio of force to mass. the ratio of force to isplacement. b d the 'inetic energy of the spring. the potential energy of the spring.
45.
46.
oppler wa!e. c a shoc' wa!e. d interference. e a perio.
47.
Where can you touch a staning wa!e on a rope without istur#ing the wa!e? a At a noe b At any place along the wa!e c At an antinoe
48.
taning wa!es can #e set up a in organ pipes. b #y #lowing across the top of a soa #ottle. c on strings of musical instruments. d all of the a#o!e e none of the a#o!e
Problem 49.
A spring stretches #y 25.0 cm when a 0.500-'g mass is suspene from its en. a. >etermine the spring constant. #. 7ow much elastic potential energy is store in the spring when it is stretche this far?
50.
A spring has a spring constant of 1$5 N/m. 7ow far must it #e compresse so that &.$% 6 of elastic potential energy is store in the spring?
51.
n a planet where the gra!itational acceleration is fi!e times g on @arth( a penulum swings #ac' an forth with a perio of 1.22 s. What is the length of the penulum?
52.
onya hears water ripping from the ea!es of the house onto a porch roof. he counts $0 rops in 1.0 min. a. What is the frequency of the rops? #. What is the perio of the rops?
53.
A o!e wa!eBone of the four types of wa!es associate with earthqua'esBis a trans!erse wa!e in which the surface of @arth mo!es #ac' an forth as the wa!e passes. What is the spee of a o!e wa!e that has a perio of 150 s an a wa!elength of 20 'm?
54.
A pulse with an amplitue of 0.5$ m tra!els to the right along a rope. Another pulse( with an amplitue of C0.2& m( tra!els to the left along the same rope. The two pulses approach each other. What is the amplitue of the rope at the point where the mipoints of the pulses pass each other?
55.
A physics teacher attaches an electric oscillator to one en of a 2.0-m hori+ontal spring an attaches the other en of the spring to a stationary hoo' in the wall. he austs the frequency of the oscillator to prouce a staning wa!e in the spring. tuents o#ser!e that the staning wa!e has three noes an two antinoes. he then ou#les the frequency of the oscillations an prouces another staning wa!e. 7ow many noes an antinoes o the stuents o#ser!e in the new staning wa!e?
56.
The istance #etween four consecuti!e antinoes of a staning wa!e in a spring is &2 cm. What is the wa!elength of the staning wa!e ?
57.
An astronaut lans on an un'nown planet an must etermine the !alue of the gra!itational acceleration g using a !ariety of sur!ey instruments. a. ne instrument rests on the groun an shoots a #all !ertically with a 'nown spee. ,f the astronaut measures the time the #all ta'es to rise from its launch position( an the time the #all ta'es to fall #ac' to the launch position( can the astronaut etermine the !alue of g ? Why or why not? #. Another instrument is a simple unmar'e weight suspene from a spring with constant k 22.5 N/m.
58.
A simple penulum has an arm that is 20.0 cm long with a 100.0-g mass suspene from the en. Dulling the mass 2.0 cm to one sie an releasing it starts the penulum in motion. a. What is the amplitue of this penulum? #. What is the perio of this penulum? c. ,f the arm is lengthene to 50.0 cm( what happens to the perio? . ,f the mass is increase to 500.0 g( what happens to the perio? e. ,f the mass is pulle &.5 cm to one sie an release( what happens to the perio? f. A granfather cloc' uses a penulum with a perio of 2.0 s to 'eep time. ,f the cloc' uses a 25-g mass as a counterweight( how long shoul the penulum arm #e?
59.
A spring is su#ecte to a stretching force. The following graph shows the !ariation of the force with the e*tension prouce in the spring.
60.
The graph #elow isplays how isplacement !aries with time when a wa!e passes a fi*e point at a spee of 12.0 m/s.
Practice Test Vibrations and Waves Answer Section MULTIPLE CHOICE 1.
ANS:
B
DIF:
1
2.
ANS:
C
DIF:
1
3.
ANS:
D
DIF:
2
4.
ANS:
C
DIF:
3
5.
ANS:
D
DIF:
2
6.
ANS:
C
DIF:
2
7.
ANS:
C
DIF:
2
8.
ANS:
B
DIF:
2
9.
ANS:
D
DIF:
2
10.
ANS:
D
DIF:
2
11.
ANS:
A
DIF:
3
12.
ANS:
C
DIF:
2
13.
ANS:
C
DIF:
2
14.
ANS:
B
DIF:
2
15.
ANS:
D
DIF:
2
16.
ANS:
D
DIF:
1
17.
ANS:
A
DIF:
2
18.
ANS:
A
DIF:
2
19.
ANS:
D
DIF:
2
20.
ANS:
C
DIF:
2
21.
ANS:
B
DIF:
2
22.
ANS:
A
DIF:
3
23.
ANS:
B
DIF:
1
24.
ANS:
C
DIF:
2
25.
ANS:
D
DIF:
2
26.
ANS:
A
DIF:
3
27.
ANS:
A
DIF:
1
28.
ANS:
C
DIF:
1
29.
ANS:
B
DIF:
1
30.
ANS:
D
DIF:
1
31.
ANS:
C
DIF:
1
32.
ANS:
D
DIF:
1
33.
ANS:
D
DIF:
2
34.
ANS:
C
DIF:
2
35.
ANS:
B
DIF:
2
36.
ANS:
B
DIF:
2
37.
ANS:
A
DIF:
2
38.
ANS:
B
DIF:
2
39.
ANS:
C
DIF:
3
40.
ANS:
C
DIF:
2
41.
ANS:
C
DIF:
1
42.
ANS:
B
DIF:
1
43.
ANS:
A
DIF:
2
44.
ANS:
D
45.
ANS:
C
46.
ANS:
D
DIF:
L1
47.
ANS:
A
DIF:
L2
48.
ANS:
D
DIF:
L2
PROBLEM 49.
ANS:
a. F = κξ
κ = Φ ξ Φ = µ γ = (0.500κγ)(9.80µ /σ2) = 4.90Ν
κ = 4.90 Ν 0.250 µ = 19.6Ν/µ β.ΠΕ σπ = 1 κξ 2 2 = (19.6Ν/µ )(0.250µ ) 2 = 0.612ϑ 50.
ANS:
PE sp =
2ΠΕ σπ
ξ = =
1 κξ 2 2
κ 2(4.39ϑ)
135N/m
=0.255m 51.
ANS:
T = 2π
Ι γ
Ê ˆ˜2 Á ˜ Τ Á λ = γ Á Á 2π ˜˜ Ë ¯ Ê ˆ˜2 Á ˜ 1.22s Á =5(9.80m/s )Á ˜ Á Ë 2π ˜¯ 2
=1.85m 52.
ANS:
a. f =
Ê Á ˜˜Ê 30 δροπσ ˆ 1min ˆ˜˜˜ Á Á Á ˜˜Á Á Á Á Á 1.0 µ ιν ˜Ë 60s ˜¯ Ë ¯
=0.50Hz b. T = 1 = f
1 0.50Hz
=2.0s 53.
ANS:
v = λφ
φ = 1 Τ ϖ = λ Τ 5
= 6.2× 10 µ 150 σ = 4.1 × 10 3µ /σ= 4.1κµ / 54.
ANS:
A A1 A2 0.5$ m 3C0.2& m4 0.2% m 55.
ANS:
;or f 1( there are three noes an two antinoes( inicating that the staning wa!e has a wa!elength of 2.0 m( the same as the length of the spring.
λ 1 2.0m 2 f 1
2
v λ 1 f 1 λ 2 f 2 λ 2
f 1 f 2
f 1
2 f 1
λ 1
λ 1
λ 1
2
2.0 m 1.0m 2 The new staning wa!e has a wa!elength of half the length of the spring. The spring contains two full wa!elengthsE therefore( the stuents o#ser!e fi!e noes an four antinoes. 56.
ANS:
The istance #etween four antinoes represents 1.5 λ . 1.5λ = 42χµ
λ = 42 χµ = 28χµ 1.5 57.
ANS:
a.
Fes. ;rom proectile motion( t rise =
ϖ ψι γ
, ορτ τοταλ = 2τ ρισε =
2ϖ ψι
γ
.
:ecause the initial spee is 'nown( an the irection the #all is launche is !ertical( once the astronaut measures the time( s/he can calculate the !alue of y. g =
2ϖ ψι
τ τοταλ
.
#. No. The mass of the weight is not 'nown. nly the spring constant is 'nown8 F g mg an F −kx mg −kx g = − κξ
µ
There are not enough 'nown quantities to etermine the !alue of g .
Á 1min ˜˜˜ Á47 χψχλεσ/µ ιν ˜ˆÁ =Ê Á ˜ Ë ¯Á Ë 60s ¯
=0.7833Hz T= 1 =1.277s f
T2 =4π 2 l
c.
g
g =4π 2 l2 T
Ê ˆ˜ Á Á ˜˜ Ê ˆ 2˜ 0.500m Á Á ˜ =Á4π ˜Á Á 2 Á Ë ¯Á (1.277s) ˜˜˜ Ë ¯ =12.1m/s2 58.
ANS:
a.
The amplitue is the istance of the swing from the center line( A 2.0 cm. T = 2π
#.
λ γ
= 0.898 σ c.
:ecause the perio an length of the penulum arm are irectly relate( an increase in the arm length increases the perio8
λ γ
T = 2π
= 1.42 σ .
Nothing. The perio( T ( is not epenent upon the mass of the penulum.
λ γ
T = 2π e.
Nothing. The perio( T ( is not epenent upon the amplitue. T = 2π
λ γ
T = 2π
λ γ
Τ 2 = 4π 2 λ γ 2
f. λ = Τ γ
4π 2
Ê (2.0 σ)2Á Á9.80m/s2 ˜˜ˆ Ë ¯ = 2 4π =0.99m
59.
ANS: −2 2.0 × 10 6
DIF: 60.
3
ANS:
;requency 0.&00 7+ Wa!elength $0.0 m DIF:
3
