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.

Show that when a string fixed at its two ends vibrates in 1 loop, 2 lo

1.	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.
Answer» Solution : 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`