Consider three speakers, A, B, and C, equally spaced along a line, as shown belo
ID: 2277809 • Letter: C
Question
Consider three speakers, A, B, and C, equally spaced along a line, as shown below. Alistener is positioned directly across from speaker B, at a position dB = 10m, and hears
intensities IA = I0, IB = I0/4, and IC = I0 from A, B, and C, respectively, when one speaker
at a time is turned on. The speakers are all driven in phase at a frequency of 800 Hz, and
the speed of sound is 330 m/s.
A B C
Listener (distance to B is 10m)
1. What is the minimum distance, d, the listener can be from speakers A and C so that
she hears all three waves arrive in phase?
a. d = 10.4 m
b. d = 14.1 m
c. d = 20.0 m
2. What total intensity does the listener hear, assuming the waves arrive in phase?
a. Io/4
b. 9Io/4
c. 25Io/4
3. The listener now adds a phase shift to speaker B so that she hears a total intensity of
ITot = 5I0 from the three speakers. What phase shift did she add?
a. It is not possible to add a phase shift that gives this total intensity.
b. Consider three speakers, A, B, and C, equally spaced along a line, as shown below. A
listener is positioned directly across from speaker B, at a position dB = 10m, and hears
intensities IA = I0, IB = I0/4, and IC = I0 from A, B, and C, respectively, when one speaker
at a time is turned on. The speakers are all driven in phase at a frequency of 800 Hz, and
the speed of sound is 330 m/s.
A B C
Listener (distance to B is 10m)
1. What is the minimum distance, d, the listener can be from speakers A and C so that
she hears all three waves arrive in phase?
a. d = 10.4 m
b. d = 14.1 m
c. d = 20.0 m
2. What total intensity does the listener hear, assuming the waves arrive in phase?
a. Io/4
b. 9Io/4
c. 25Io/4
3. The listener now adds a phase shift to speaker B so that she hears a total intensity of
ITot = 5I0 from the three speakers. What phase shift did she add?
a. It is not possible to add a phase shift that gives this total intensity.
b.
Explanation / Answer
we know from the relation
(I1/I2) = (r2/r1)^2
where I1 and I2 are intensities and r1 and r2 are their distances