Question

The speed of wave on a string with a fixed end and a free end is 300 m/s. The frequency of a wave is 250Hz. Find the length of the string necessary to produce a standing wave with first harmonic.

Answer 1

The wavelength of a standing wave

$$\lambda=\frac{v}{f}=\frac{300\:\rm m/s}{250\:\rm Hz}=1.2\:\rm m$$

The length of the string

$$L=\frac{1}{4}\lambda=\frac{1}{4}\times 1.2\:\rm m=0.3\: m$$