A string, fixed at both ends, vibrates in a resonant mode with a separation of 2 0 cm between the consecutive nodes. For the next higher resonant frequency, this separation is reduced to 1 6 cm. Find the length of the string.

Question

Philoid · Accepted Answer

80 cm

Suppose, there are n loops initially and length of loop is L.

So,

So, L_l=

₂=

Computing this we get,

n=4

So, length of the string is,

A string, fixed at both ends, vibrates in a resonant mode with a separation of 20 cm between the consecutive nodes. For the next higher resonant frequency, this separation is reduced to 16 cm. Find the length of the string.