Descripción: Solution file for youtube video "Server Error in '/' Application Solution"
Full description
11Descripción completa
Question: You are standing 2.5 m directly in front of one of the two loudspeakers shown in the figure. They are 3.0 m apart and both are playing a 686 Hz tone in phase. As you begin to walk directly away from the speaker, at what distances from the speaker do you hear a minimum sound intensity? 0
The room temperature is 20 C. .
Answer: Frequency of sound f = 686 Hz 0
Speed of sound at 0 C, V0 = 331 m/s 0
Therefore, speed of sound at 20 C, V = V0 + 0.61t = 331 + 0.61 x 20 = 343.2 m/s . Wavelength of sound, = = = 0.50 m The minimum sound will be heard at positions at which the path difference between the waves coming
from the two speakers is an odd number multiple of , i. e. (2n 1) , where n = 1, 2, 3, ----- From the figure, path difference = BC – AC = + Thus,
+
= = (2n 1)
x
For n = 1
+ (3.0)
= = (2 x 1 1)
x
Or 9.0 √ + 9.0
= = 0.25
x
Or 9.0 = 0.25 + √ + 9.0
x
Squaring both sides, we get 2
x
2
+ 9.0 = 0.0625 + x + 0.50 x
Or = =
x
.. = 17.875 m .
.
x
Similarly for n = 2
+ (3.0)
= (2 x 2 1)
x
.
Or
√ + 9.0
= 0.75
x
Or
√ + 9.0 = 0.75 +
x
Squaring both sides, we get 2
x
2
+ 9.0 = 0.5625 + x + 1.50 x
Or =
x
.. = 5.625 m .
Similarly for n = 3
+ (3.0)
= (2 x 3 1)
x
.
Or
√ + 9.0
= 1.25
x
Or
√ + 9.0 = 1.25 +
x
Squaring both sides, we get 2
x
2
+ 9.0 = 1.5625 + x + 2.50 x
Or =
x
.. = 2.975 m .
Hence, minimum sound intensity is heard at 2.975 m, 5.625 m and 17.875 m from the speaker A.
