Question

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.

Answer 1

If P and (P + 1) be the number of loops corresponding to two consecutive resonances, then length of string 

L = P × 2 

= (P + 1) × 1.6 

∴ P = 4 

and L = 8.0 cm