Question

There are three sources of sound of equal intensity with frequencies 400, 401, 402 vibrations/sec. The number of beats heard per second is

• A. 1
• B. 2
• C. 3
• D. 0

Answer 1

The correct option is A 1

Resultant displacement of the wave by these three wave is
$y=asin2\pi 400t+asin2\pi 401t+asin2\pi 402t$
$y=a(1+2cos2\pi t)sin2\pi 401t$
So the resultant magnitude $a(1+2cos2\pi t)$ has a maximum when,
$cos2\pi t=1$
or, $t=0,1,\mathrm{2...}$
The time interval between two successive maximum is 1 sec.
So beat frequency is 1sec.