- #1

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Can you explain me the significance of the above equation in the context of waves and oscillations? It's something to do with 'beats,'.

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- #1

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Can you explain me the significance of the above equation in the context of waves and oscillations? It's something to do with 'beats,'.

- #2

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- #3

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- #4

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Yes sir, they derived it from $$y_{1}=A \sin \omega_{1} t ; y_{2}=A \sin \omega_{2} t$$

- #5

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How to proceed ahead from here?

- #6

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Sorry, what do you mean? Are you familiar with common trig identities like the sum of two sine waves?

How to proceed ahead from here?

https://www.purplemath.com/modules/idents.htm

- #7

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Duplicate thread starts merged into one thread

Consider two two sinusoids at different frequencies $$y_{1}=A \sin \omega_{1} t ; y_{2}=A \sin \omega_{2} t$$

$$y=y_{1}+y_{2}=A\left[\sin \omega_{1} t+\sin \omega_{2} t\right]=A\left[2 \sin \left(\frac{\omega_{1}+\omega_{2}}{2}\right) t \cos \left(\frac{\omega_{1}-\omega_{2}}{2}\right) t\right]$$

For the formation of waxing, A is maximum, what will be the time period? And for the formation of wanning, A is minimum, what will be the time period?

This is from my class notes. Unfortunately, I missed my class and I am not able to understand now. So I have turned to Physics Forums for help.

Please explain me how the time period for the formation of beat T, $$T=\dfrac{1}{\nu_{1}+\nu_{2}}$$

and the beat frequency $$n=\nu_{1} \sim \nu_{2}$$

$$y=y_{1}+y_{2}=A\left[\sin \omega_{1} t+\sin \omega_{2} t\right]=A\left[2 \sin \left(\frac{\omega_{1}+\omega_{2}}{2}\right) t \cos \left(\frac{\omega_{1}-\omega_{2}}{2}\right) t\right]$$

For the formation of waxing, A is maximum, what will be the time period? And for the formation of wanning, A is minimum, what will be the time period?

This is from my class notes. Unfortunately, I missed my class and I am not able to understand now. So I have turned to Physics Forums for help.

Please explain me how the time period for the formation of beat T, $$T=\dfrac{1}{\nu_{1}+\nu_{2}}$$

and the beat frequency $$n=\nu_{1} \sim \nu_{2}$$

- #8

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Yes sir, I know, I solved it, How to solve for time period now? I am not able to understand thisSorry, what do you mean? Are you familiar with common trig identities like the sum of two sine waves?

https://www.purplemath.com/modules/idents.htm

View attachment 295097

- #9

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Which time period? The sound you hear when listening to audio beats is the sum frequency, modulated at the difference frequency. So the period of the beats (the louder-softer characteristic) is at the difference frequency of the two sine waves.How to solve for time period now?

- #10

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Yes, I think the time period of the beats. Does the time period depend on A? When the A is maximum, $$t=\dfrac{n}{\nu_1-\nu_2}$$, When A is minimum $$t=\dfrac{2n+1}{2 \left( \nu_1-\nu_2 \right)}$$.Which time period? The sound you hear when listening to audio beats is the sum frequency, modulated at the difference frequency. So the period of the beats (the louder-softer characteristic) is at the difference frequency of the two sine waves.

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