Solving Sound Problems: Beats, Interference & Wavelengths

[Gauss177]

Homework Statement

1. How many beats will be heard if two identical flutes each try to play middle C (262 Hz), but one is at 0.0 deg C and the other is at 20.0 deg C?

2. Two loudspeakers are 2.5 m apart. A person stands 3.0 m from one speaker and 3.5 m from the other. a) What is the lowest frequency at which destructive interference will occur at this point? b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest).

3. A source emits sound of wavelenghts 2.80 m and 3.10 m in air. a) How many beats per second will be heard (assume T = 20 deg C)? b) How far apart in space are the regions of maximum intensity?

Homework Equations

The Attempt at a Solution

1. It says middle C is 262 Hz, but is this at 20 deg C or 0 deg C? I think this needs to be known to figure out the frequency at each temperature.

2. I've only seen an example of this kind of problem where the frequency of sound emitted is given, so I'm not sure what to do about this problem. But for (b) I think that destructive interference occurs every half wavelength.

3. For (a) I used the v=(freq)(wavelength) equation and plugged in the given wavelengths and speed of sound (343 m/s) to find the frequencies to be 122.5 and 110.6 Hz, so I found the beats will be heard at 11.9 Hz. I'm not sure how to do (b) though, but is the answer .084 (it occurs every time a full wavelength passes)?

Thanks for the help.

 

[G01]

1.The frequency given is probably given for standard temperature, which is 0C.

2. You are correct that the waves need to be separated by half a wavelength for destructive inteference:

The waves each travel a different distance to the observer, r. For there to be destructive interference:

$$\Delta r = (n + 1/2)\lambda$$

Now if you want the shortest frequency, you want the longest wavelength correct? What does this force the interger n to be? See how far you can get now.

3. This question is asking for the beat frequency(beats per min.):

$$f_{beat}=f_1-f_2$$Good Luck!

 

[Gauss177]

Thanks G01. I think I did 3a correctly, but how do you do 3b?

 

[denverdoc]

well assume the beat frequency exists independent of all else, how would the peaks be spaced?