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Question: Beats are produced by two waves given by \(y_{1} = a\sin 2000\pi t\) and \(y_{2} = a\sin 2008\pi t\)...

Beats are produced by two waves given by y1=asin2000πty_{1} = a\sin 2000\pi t and y2=asin2008πty_{2} = a\sin 2008\pi t. The number of beats heard per second is

A

Zero

B

One

C

Four

D

Eight

Answer

Four

Explanation

Solution

Number of beats per second = n1n2n_{1}\sim n_{2}

ω1=2000π=2πn1\omega_{1} = 2000\pi = 2\pi n_{1} ⇒ n1 = 1000

and ω2=2008π=2πn2\omega_{2} = 2008\pi = 2\pi n_{2} ⇒ n2 = 1004

Number of beats heard per sec =10041000=4= 1004 - 1000 = 4