# Sound waves - Detector and a moving wall

1. Apr 8, 2013

### Saitama

1. The problem statement, all variables and given/known data
A sound source, detector and a movable wall are arranged as shown in the figure. In this arrangement detector is detecting the maximum intensity. If the speed of sound is 330 m/s in air and frequency of source is 600 Hz, then find the distance by which the wall should be moved away from the source, so that detector detects minimum intensity.

2. Relevant equations

3. The attempt at a solution
I don't quite understand the situation. Do the waves reflected by the wall ever reach the detector? I don't see how the reflected waves would reach the detector. (Can I assume that the waves get reflected the same way as a light ray would? )

Any help is appreciated. Thanks!

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2. Apr 8, 2013

### ehild

Have you experienced echo in your life? All waves can reflect....

ehild

3. Apr 8, 2013

### Saitama

Yes, I have experienced it but for that the reflected waves should reach the detector. But here they don't.

4. Apr 8, 2013

### ehild

Why not? The reflected wave travels backwards.

ehild

5. Apr 8, 2013

### Saitama

So the sound waves don't reflect as the light rays would?

6. Apr 8, 2013

### ehild

They reflect the same way, but here the incidence is normal. That sound source can be a loudspeaker, not a "point source"

7. Apr 8, 2013

### Saitama

Okay but how should I begin making the equations?

8. Apr 8, 2013

### ehild

Think. How can the sound arrive by two different ways to the detector?

ehild

9. Apr 8, 2013

### Saitama

By reflection and directly from the source.

10. Apr 8, 2013

### ehild

And what is the path difference?

11. Apr 8, 2013

### Saitama

For constructive interference or maximum intensity, it is $n\lambda$ and for destructive interference or minimum intensity it is $\displaystyle \left(n+\frac{1}{2}\right)\lambda$ but I still have no idea what am I supposed to do with this.

12. Apr 8, 2013

### ehild

What is the geometric path difference between the reflected wave and the directly arriving wave at the detector? And consider the phase change at the wall, too.

ehild

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• ###### soundref.JPG
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13. Apr 8, 2013

### Saitama

There will be a phase change of $\pi$ which corresponds to a path difference of $\frac{\lambda}{2}$.
$$\Delta p=\left(d+x+\frac{\lambda}{2}\right)-(d-x)$$
$$\Delta p=2x+\frac{\lambda}{2}$$
Is this correct?

14. Apr 8, 2013

### ehild

Yes.

15. Apr 8, 2013

### Curious3141

Will there be a phase change at the wall? It's of higher acoustic impedance than the air.

16. Apr 9, 2013

### Saitama

I just checked my notes. It says that there will be no phase change when the wave is reflected from the rigid boundary.

Should I make the equations again?

17. Apr 9, 2013

### Curious3141

Of course, if there's a change in your assumptions, there'll be a change in your equations.

18. Apr 9, 2013

### ehild

Yes. Omit the Lambda/2.

19. Apr 9, 2013

### Saitama

Since there is no phase change, for maximum intensity,
$$2x=n\lambda$$
For destructive interference
$$2x'=\left(n+\frac{1}{2}\right)\lambda$$
Change in distance between the detector and wall
$$\Delta x=x'-x=\frac{\lambda}{4}$$
$$\Delta x=0.125 m$$

Thanks a lot both of you, this is the right answer.

20. Apr 9, 2013

### Curious3141

Isn't $\displaystyle \frac{\lambda}{4} = 0.1375m$?

$\displaystyle \lambda = \frac{v}{f} = \frac{330ms^{-1}}{600s^{-1}} = 0.55m$