Question

prove that the beat frequency is the difference of frequencies of two waves which superimpose giving beats.​

Answer 1

Explanation:

the interference to become maximally constructive is the beat period

TBEAT=n×TS – (2)

From 1 & 2, We get

TBEAT=TLΔT TS

Here ΔT=TL–TS

So, TBEAT=TLTL–TSTS

TBEAT=TLTSTL–TS

Dividing top and bottom by the product TLTS gives,

TBEAT=11TS–1TL

Taking reciprocal both sides we get,

1TBEAT=1TS–1TL

Now, by using the relation between f = 1T we get,

fBEAT=|f2–f1|

The above equation is the beat frequency formula of two waves.