Questions

A wire of density 9 $\times$ 10³ kg/m³ is stretched between two clamps 1 m apart and is stretched to an extension of 4.9 $\times$ 10^-4 m. Young's modulus of material is 9 $\times$ 10¹⁰N m. Then:

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The lowest frequency of standing wave is 35 Hz

The frequency of 1st overtone is 70 Hz

The frequency of 1st overtone is 105 Hz

The stress in the wire is 4.41 × 107 N/m2

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detailed solution

Correct option is A

Speed of wave in wireV=TρA=YΔllA×1ρA=YΔllρMinimum frequency; that means fundamental mode.f=Vλ=V2l=12lYΔllρ=35Hz Stress =YΔll=9×1010×4.9×10−41=4.41×107N/m2and frequency of first overtone = 2f=70 Hz.

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