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Show that when a string fixed at its two...

Show that when a string fixed at its two ends vibrates in 1 loop, 2 loops, 3 loops and 4 loops, the frequencies are in the ratio 1 : 2:3: 4.

Text Solution

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In case of stationary waves, frequency in the `n^(th)` mode of vibration is,
`f _(n) = (2n)/(2L)` (Where `v = sqrt ((T)/( mu))` = speed of transverse wave in stretched string)
`therefore f _(n) prop n `
`implies f _(1) :f_(2) :f _(3) :f_(4) = 1:2:3:4`
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