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Q.

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

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a

The lowest frequency of standing wave is 35 Hz

b

The frequency of 1st overtone is 70 Hz

c

The frequency of 1st overtone is 105 Hz

d

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

answer is A.

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Detailed Solution

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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