Three tuning forks of frequencies n - x , n and n + x are vibrated simultaneously . If the amplitudes of vibration are equal , show that the forks would form beats .

Answer

Let A be the amlitude of vibration of each tuning fork .
Then, the equations of the waves are `y_(1) = A sin 2 pi (n - x) t, y_(2) = A sin 2 pi n t and y_(3) = a sin 2 pi (n + x ) t ` .
`y = y_(1) + y_(2) + y_(3)`
` = A [ sin 2 pi (n - x ) t + sin 2 pi n t + sin 2 pi (n + x) t ] `
` = A [ { sin 2 pi (n + x) t + sin 2 pi (n - x) t } + sin 2 pi n t]`
` = A [ 2 sin 2 pi n t cos 2 pi x t + sin 2 pi n t ] `
` = A (1 + 2 cos 2 pi x t ) sin 2 pi n t `
`:.` The amplitude of the r esultant wave ` = A (1 + 2 cos 2 pi x t)` This amplitude clearly depends on time. As result, the intensity of the emitted sound would also increase and decrease periodically with time [ ` :' ` intensity `prop ("amplitude")^(2) `] . Thus beats are produced . SO, beats can be produced not only due to superposition of two waves, but also due to superposition of more than two waves .