Question

A student wants to establish a standing wave on a wire 1.8 m long clamped at both ends. If the wave speed is 72 m/s, what is the minimum frequency she should apply to set up standing waves?

20 Hz

12 Hz

24 Hz

15 Hz

18 Hz

Answer 1

$\frac{2l}{v}=nT\implies \frac{2l}{\lambda}=n,$

$\nu=\frac 1T=\frac{v}{\lambda}=\frac{v}{2l}n,$

$\nu_{min}=\nu_{n=1}=\frac{v}{2l}=\frac{72}{2\cdot 1.8}=20~Hz.$