# Sound Intensity Peak

1. Dec 2, 2013

### woaini

1. The problem statement, all variables and given/known data

One wheel goes at 850 rpm and the other at 780 rpm, and obviously they make a noise. Standing in an enclosed room, you hear the sound intensity increase and then decrease periodically due to wave interference. How long does it take between successive times for the sound intensity to reach a peak?

f1= 850
f2= 780
Vs =343 m/s

2. Relevant equations

λ=Vs/f

3. The attempt at a solution

343/850=0.40
343/780=0.44

So how do I find a peak? Does it have something to do with constructive interference?

2. Dec 2, 2013

Yes.

3. Dec 2, 2013

### woaini

What do you mean yes... What method would I use to find the peak between successive times?

4. Dec 2, 2013

### CWatters

I mean yes it's to do with constructive interference.

If you were to draw two sin waves to scale you would find they would go in and out of sync due to the difference in frequency. A peak on one won't always coincide with the peak of the other. When it does the result will sound louder. It's easy to see this when the frequencies are a multiple of each other...

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/beat.html

5. Dec 2, 2013

### woaini

Is there an equation to combine the two frequencies?

6. Dec 2, 2013

### CWatters

See that link I posted..

but note the question askes for a time not a frequency.

7. Dec 2, 2013

### woaini

So am I suppose to find the beat frequency of the two waves then determine the time?

E.g. 850-780=70RPM

T=1/f = 0.014s

Or do I have to convert the RPM to Hz and then find time?

70RPM=1.167Hz

T=0.856898s

Last edited: Dec 3, 2013
8. Dec 3, 2013

### CWatters

What do you think? What are the units of Frequency? Work out the two frequencies first.

9. Dec 3, 2013

### woaini

I guess frequency then. Why would I need to workout the two frequencies first? Wouldn't finding the difference and converting be faster?

10. Dec 3, 2013

### CWatters

You could do that but the thing to remember is that the beat frequency is the difference between the two frequencies. Other problems may not make any reference to rpm.

So in summary.. They produce two tones, one at 14.17Hz and 13Hz. The beat frequency is the difference or 14.17-13 = 1.17Hz (Which is the answer you got). The time period between successive peaks in sound intensity is therefore 1/1.17 = 0.85seconds.

11. Dec 3, 2013