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

Answer

1 Hz

Explanation

Let the SHM equations ofthese given frequencies are
`y_(1) = A sin(800pit)`
`y_(2) = A sin(802pit)`
`y_(3) = A sin(804pit)`
Resulting oscillation displacement is given as
`y_(R) = y_(1) + y_(2) + y_(3)`
= `A [sin(800pit) + sin(802 pit) + sin(804pit)]`
= `A [sin(800pit) + 2sin(802 pit) + sin(804pit)]`
`A[1 + 2 cos(2pit)]`
= `R sin (802pit)`
Thus resulting sound is of average frequency 401 Hz and time varying amplitude given as
`R = A(1 + 2 cos(2pit))`
Hee R will be maximum when
`cos 2pie t = +1`
`2pit = 2Npi`
= t = n Thus at t = 0, 1, 2 .... time instants maxima occurs so beat period here is ls so beat frequency is given as
`f_(B) = (1)/(T_(B))` = 1 Hz