Question

A string 1m long is fixed at one end. The other end is moved up and down with frequency 15 Hz. Due to this, a stationary wave with four complete loops, gets produced on the string. Find the speed of the progressive wave which produces the stationary wave. [Hint: Remember that the moving end is an antinode.]

Answer 1

Given : L = 1 m, n = 15 Hz.

The string is fixed only at one end. Hence, an antinode will be formed at the free end. Thus, with four and half loops on the string, the length of the string is

L = \(\frac{λ}{4}+4\frac{λ}{2}=\frac{9}{4}λ\)

∴ λ = \(\frac{4L}{9}\) =\(\frac{4}{9}×1\)

v = n λ

∴ Speed of the progressive wave

v =15 x\(\frac{4}{9}\)= 6.667 m/s