Two tuning forks (X ) and (Y ) are of frequencies (280 ~Hz ) and (284 ~Hz ). A third tuning fork (Z ) is of unknown frequency. When (X ) and (Z ) are sounded together certain beats are heard per second. When (Y ) and (Z ) are sounded togeth

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Two tuning forks (X ) and (Y ) are of frequencies (280 ~Hz ) and (284 ~Hz ). A third tuning fork (Z ) is of unknown frequency. When (X ) and (Z ) are sounded together certain beats are heard per second. When (Y ) and (Z ) are sounded together beat frequency is found to be thrice as great. The frequency of (Z ) is

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Correct answer: D. (278 ~Hz )

Given, frequency of tuning fork (X ) and (Y ) are, ( aligned & n_X=280 ~Hz & n_Y=284 ~Hz & n_Z=? aligned ) When tuning forks (X ) and (Z ) are sounded together, then beats produced is (b ) (assume). ( n_Z-n_X=b ) ...(i) Again, when (Y ) and (Z ) are sounded together, then (n_Z-n_Y=3 b ) ...(ii) Dividing Eq. (i) by Eq. (ii), we have ( array ll & n_Z-n_X n_Z-n_Y = b 3 b n_Z-280 n_Z-284 = 1 3 & 3 n_Z-840=n_z-284 & 3 n_z-n_Z=840-284 & 2 n_Z=556 n_Z=278 ~Hz array )

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