Frequency of Resultant Waves

[justadream]

TPR SW claims that the frequency of resultant wave (summing up 2 waves) should be the same as the frequency of the individual waves.

I think in this example, TPR is referring to 2 individual waves that have the same frequency.

But what about when you sum up 2 waves with different frequencies? What is the frequency of the resultant wave?

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[DrknoSDN]

But what about when you sum up 2 waves with different frequencies? What is the frequency of the resultant wave?

If you superimpose two waves of different frequencies you will end up with a beat frequency equal to the difference of their frequencies.

The frequency of the resultant wave of 2 waves that are the same frequency is the same as the original because the pattern of constructive and destructive interference would repeat each wavelength.

 

[dnrs]

The frequency of the resultant wave is the average of the frequencies of the waves that make it up.

 

[DrknoSDN]

The frequency of the resultant wave is the average of the frequencies of the waves that make it up.

I am inclined to disagree.

Maybe I am not thinking about resultant wave correctly but if you have 10Hz and 9Hz sine waves the resultant wave to me seems like it would be a 1 Hz wave and not 9.5 Hz.
Clarification appreciated. ty

 

[dnrs]

I am inclined to disagree.

Maybe I am not thinking about resultant wave correctly but if you have 10Hz and 9Hz sine waves the resultant wave to me seems like it would be a 1 Hz wave and not 9.5 Hz.
Clarification appreciated. ty

Two sine waves with different frequencies: Beats
Two waves of equal amplitude are travelling in the same direction. The two waves have different frequencies and wavelengths, but they both travel with the same wave speed. Using the principle of superposition, the resulting particle displacement may be written as:

This resulting particle motion is the product of two travelling waves. One part is a sine wave which oscillates with the average frequency f = ½(f1 + f2). This is the frequency which is perceived by a listener. The other part is a cosine wave which oscillates with the difference frequency f = ½(f1 - f2). This term controls the amplitude "envelope" of the wave and causes the perception of "beats". The beat frequency is actually twice the difference frequency, fbeat = (f1 - f2).

 

[DrknoSDN]

Yup, I was thinking about the frequency of the beat specifically and not the frequency from crest to crest. Ty

http://www.acs.psu.edu/drussell/demos/superposition/superposition.html
http://clas.mq.edu.au/speech/acoustics/waveforms/adding_waveforms.html

 

[justadream]

So just to clarify, is the frequency of the resultant wave the frequency of the beats produced by the 2 original waves?

 

[DrknoSDN]

So just to clarify, is the frequency of the resultant wave the frequency of the beats produced by the 2 original waves?

No. Documents online more often talk about a "resultant wave" as being the average of the two wave frequencies, or the frequency of each crest to crest in the new waveform.
(the beat frequency is just the oscillation in amplitude of the resultant wave)

 

[justadream]

@DaknoSDN

Thanks for the reply.

I'm still a but confused after reading over this statement from your second link (http://clas.mq.edu.au/speech/acoustics/waveforms/adding_waveforms.html)

"The highest common factor of 100, 200 and 300 is 100 and so the resultant complex wave has a fundamental frequency of 100 Hz."

Why are they talking about highest common factors?