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Question

# A steel wire of mass 8 g and length 160 cm is fixed at two ends. The tension in the wire is 50 N. Find the frequency and wavelength of the fourth harmonic.

A
125 Hz,40 cm
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B
250 Hz,40 cm
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C
125 Hz,80 cm
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D
250 Hz,80 cm
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Solution

## The correct option is C 125 Hz,80 cmGiven that m=8 g or 8×10−3 kg l=160 cm or 1.6 m T=50 N So , Linear mass density (μ)=ml=8×10−31.6=0.5×10−2 kg/m Now, Wave speed (v)=√500.5×10−2=100 m/s For fourth harmonic, f4=4v2l=4×1002×1.6=125 Hz and For wavelength, λ=vf=100125=0.8 m or 80 cm Thus, option (c) is the correct answer.

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