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
2lv=nT ⟹ 2lλ=n,\frac{2l}{v}=nT\implies \frac{2l}{\lambda}=n,v2l=nT⟹λ2l=n,
ν=1T=vλ=v2ln,\nu=\frac 1T=\frac{v}{\lambda}=\frac{v}{2l}n,ν=T1=λv=2lvn,
νmin=νn=1=v2l=722⋅1.8=20 Hz.\nu_{min}=\nu_{n=1}=\frac{v}{2l}=\frac{72}{2\cdot 1.8}=20~Hz.νmin=νn=1=2lv=2⋅1.872=20 Hz.
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