Sound Intensity Peak: Find Time Between Peaks

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Homework Help Overview

The problem involves two wheels rotating at different speeds, generating sound waves that interfere with each other in an enclosed space. The original poster seeks to determine the time interval between peaks of sound intensity resulting from this interference.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the frequencies of the sound waves produced by the wheels and the concept of constructive interference. There is an exploration of how to calculate the time between peaks, with questions about whether to find the beat frequency or convert RPM to Hz first.

Discussion Status

The discussion is ongoing, with participants offering insights into the relationship between frequency and time. Some guidance has been provided regarding the calculation of beat frequency and its relevance to the problem, but no consensus has been reached on the best approach to take.

Contextual Notes

Participants note that the problem involves converting RPM to Hz and that the question specifically asks for a time rather than a frequency. There is also mention of potential variations in future problems that may not reference RPM.

woaini
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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?
 
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Yes.
 
What do you mean yes... What method would I use to find the peak between successive times?
 
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
 
Is there an equation to combine the two frequencies?
 
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.
 
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:
What do you think? What are the units of Frequency? Work out the two frequencies first.
 
I guess frequency then. Why would I need to workout the two frequencies first? Wouldn't finding the difference and converting be faster?
 
  • #10
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.
 
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