Interference- am I reasoning correctly?

[bcjochim07]

Homework Statement

Two loudspeakers emit sound waves along the x axis. A listener in front of both speakers hears a maximum sound intensity when speaker 2 is at the origin and speaker 1 is at x= .50 m. If speaker 1 is slowly moved forward, the sound intensity decreases and then increases, reaching another maximum when speaker 1 is at x= .90 m.

a) What is the frequency of the sound? Assume the speed of sound is 340 m/s.

b) What is the phase difference between the speakers?

Homework Equations

The Attempt at a Solution

a) The wavelength is .40 m, v=frequency*lambda 340= frequency * (.40) frequency=850 Hz

For part b, do I assume that when the speakers are .50 m apart, that is the first maximum? (meaning the phase difference is 2pi) If so then

2pi= 2pi(.50)/(.40) + initial delta phi the intial phase difference is then -pi/2, which is the correct answer. I just was wondering if I can make the assumption that I did.

 

[LowlyPion]

Homework Statement

Two loudspeakers emit sound waves along the x axis. A listener in front of both speakers hears a maximum sound intensity when speaker 2 is at the origin and speaker 1 is at x= .50 m. If speaker 1 is slowly moved forward, the sound intensity decreases and then increases, reaching another maximum when speaker 1 is at x= .90 m.

a) What is the frequency of the sound? Assume the speed of sound is 340 m/s.

b) What is the phase difference between the speakers?

Homework Equations

The Attempt at a Solution

a) The wavelength is .40 m, v=frequency*lambda 340= frequency * (.40) frequency=850 Hz

For part b, do I assume that when the speakers are .50 m apart, that is the first maximum? (meaning the phase difference is 2pi) If so then

2pi= 2pi(.50)/(.40) + initial delta phi the intial phase difference is then -pi/2, which is the correct answer. I just was wondering if I can make the assumption that I did.

Isn't the .5 m distance really the second maximum and the .9 the third? I don't think it makes any difference but the calculation is easier because with the first at .1, you are .1/.4 out of phase 2 pi/4 = pi / 2?

 

[bcjochim07]

But if the speakers are not in phase to begin with, the first maximum should lie where the phase shift is 2pi

2pi = 2pi * x/.40 - pi/2

x= .50 m, doesn't this mean that .50 is the first maximum?

 

[LowlyPion]

But if the speakers are not in phase to begin with, the first maximum should lie where the phase shift is 2pi

2pi = 2pi * x/.40 - pi/2

x= .50 m, doesn't this mean that .50 is the first maximum?

If you move the speaker back to .1 what happens?

 

[bcjochim07]

good point, I neglected the fact that the phase difference could be zero because I thought that only happened with identical sources that were right next to each other. This is a bit confusing to me.. What does a negative phase shift physically mean?

 

[LowlyPion]

good point, I neglected the fact that the phase difference could be zero because I thought that only happened with identical sources that were right next to each other. This is a bit confusing to me.. What does a negative phase shift physically mean?

That's just it. Is it a negative π/2 or a positive 3π/2?

Whatever the case, one sound source is 1/4 (2π) retarded or (1- 1/4) 2π advanced out of phase with the other - depending on perspective. It's modulo 2π whatever it is.

The sound source at the origin has traveled 1/4 Λ the distance toward you by the time it is "even" with its partner speaker to add its sound energy in lock step to continue towards you. Timewise then the sound from 2 is phase shifted (retarded) 1/4 the 2π with respect to speaker 1. This is probably the better way to look at it, taking the farther away speaker first.