Sound Intensity Peak: Find Time Between Peaks

[woaini]

Homework Statement

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

Homework Equations

λ=Vs/f

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?

 

[CWatters]

Yes.

 

[woaini]

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

 

[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

 

[woaini]

Is there an equation to combine the two frequencies?

 

[CWatters]

See that link I posted..

The beat frequency is equal to the absolute value of the difference in frequency of the two waves

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

 

[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

 

[CWatters]

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

 

[woaini]

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

 

[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.

 

[CWatters]

If you want all the maths it's here...

http://www.cmmp.ucl.ac.uk/~ahh/teaching/1B24n/lect03/node5.html#fig_beat1