A tuning fork vibrating with a sonometer having $20 cm$ wire produces $5$ beats per second. The beat frequency does not change if the length of the wire is changed to $21 cm.$ the frequency of the tuning fork (in Hertz) must be
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(c) Let the frequency of tunning fork be $N$
As the frequency of vibration string $ \propto \frac{1}{{{\rm{length}}\;{\rm{of}}{\rm{string}}}}$
For sonometer wire of length $20 cm$, frequency must be $(N + 5)$ and that for the sonometer wire of length $21cm,$ the frequency must be $(N -5)$ as in each case the tunning fork produces $5$ beats/sec with sonometer wire
Hence ${n_1}{l_1} = {n_2}{l_2}$
As the frequency of vibration string $ \propto \frac{1}{{{\rm{length}}\;{\rm{of}}{\rm{string}}}}$
For sonometer wire of length $20 cm$, frequency must be $(N + 5)$ and that for the sonometer wire of length $21cm,$ the frequency must be $(N -5)$ as in each case the tunning fork produces $5$ beats/sec with sonometer wire
Hence ${n_1}{l_1} = {n_2}{l_2}$
==> $(N + 5) \times 20 = (N - 5) \times 21$
==> $N = 205Hz.$
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