Phyiscs

Two speakers are set up 8.5m apart in an auditorium, pointing at each other. A pure sound of frequency 240Hz is being played through them. You may assume that the phase difference of the signals as they arrive at the speakers is 0. A person is standing on the line joining the speakers, 0.25m from the mid point.
The speed of sound in air is 330ms −1
(a) Calculate the phase difference as it would be detected by the person.
(b) The person moves to the mid point between the speakers (where the sound is loudest due to constructive interference), and then walks towards one speaker until the sound waves cancel out. How far do they walk until they find this point of near silence?

Reply 1

lifeofatlas.

there is definitely an easier way to do this that what ive done but anyways:
a) wavelength=330/240
= 1.375m
the person is standing 4m form one speaker (A) and 4.5m from the other (B)
4.5m/1.375 - 4m/1.375m = 0.364

to make it into degrees, 0.364x360 = 131.04 degrees

(131.04 x 2 pi)/ 360 = 2.287 pi radians

a) = 2.29 pi radians

b) the waves have to be completely in anti phase to be silent, so they have to be half a wavelength apart.
1 wavelength = 1.375m, so 1/2 wavelength = 0.6875m

from the midpoint, they have to walk 0.6875m to find the point of silence

Reply 2

Nitrotoluene

Original post by ameliephillips

It's way better if you try to figure this out on your own. Here are a few tips to get you going:
a) You have to measure the distance between the loudspeakers and after calculating the path difference to find the phase difference of the signal. If the path difference is one wavelength (λ), the phase difference is 2π radians (360°). Solve for Δϕ by substituting the path difference into the formula (2π/λ) x Δx = Δϕ.
b) Start in the middle, where the path difference is zero, and use your understanding of destructive interference to determine the point of near silence. The path difference will change as you get closer to one loudspeaker and further away from the other. The distance difference of 1/2 λ (i.e. n = 0) is the first point of near quiet.
c) By moving a distance d from the centre, you can write an equation that gives the distances (28.5 - d) and (28.5 + d). The equation is |(28.5 + d) - (28.5 - d)| = 1/2 λ because the absolute values of these distances should be 1/2 λ.
Ask any questions you have and stick to your units.
Here is my 2 cents!