Answer to Question #195523 in Mechanics | Relativity for Mohammad Balhas

Question #195523

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


1
Expert's answer
2021-05-23T18:55:26-0400

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

ν=1T=vλ=v2ln,\nu=\frac 1T=\frac{v}{\lambda}=\frac{v}{2l}n,

νmin=νn=1=v2l=7221.8=20 Hz.\nu_{min}=\nu_{n=1}=\frac{v}{2l}=\frac{72}{2\cdot 1.8}=20~Hz.


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