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(B) Let the frequencies be $n_1 = 400\, Hz$,$n_2 = 401\, Hz$,and $n_3 = 402\, Hz$.The resultant displacement $y$ is the sum of the three waves: $y = a

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$1$

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(B) Let the frequencies be $n_1 = 400\, Hz$,$n_2 = 401\, Hz$,and $n_3 = 402\, Hz$.The resultant displacement $y$ is the sum of the three waves: $y = a\sin(2\pi n_1 t) + a\sin(2\pi n_2 t) + a\sin(2\pi n_3 t)$.Using the identity $\sin A + \sin C = 2\sin(\frac{A+C}{2})\cos(\frac{A-C}{2})$,we combine the first and third terms:$y = a\sin(2\pi n_2 t) + a[2\sin(2\pi n_2 t)\cos(2\pi t)]$.$y = a(1 + 2\cos(2\pi t))\sin(2\pi n_2 t)$.The amplitude of the resultant wave is $A(t) = a(1 + 2\cos(2\pi t))$.Beats are produced by the variation in amplitude. The frequency of the amplitude variation is determined by the term $\cos(2\pi t)$.The frequency of this term is $f = 1\, Hz$.Thus,the number of beats heard per second is $1$.

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

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