Wave Motion 2 Question 12

12. A sonometer wire of length 1.5m is made of steel. The tension in it produces an elastic strain of 1. What is the fundamental frequency of steel if density and elasticity of steel are 7.7×103kg/m3 and 2.2×1011N/m2 respectively?

(a) 188.5Hz

(b) 178.2Hz

(c) 200.5Hz

(d) 770Hz

(2013 Main)

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Answer:

Correct Answer: 12. (b)

Solution:

  1. Fundamental frequency of sonometer wire

f=v2l=12lTμ=12lTAd

Here, μ= mass per unit length of wire.

Also, Young’s modulus of elasticity Y=TlAΔl

TA=YΔllf=12lYΔlldl=1.5m,Δll=0.01d=7.7×103kg/m3Y=2.2×1011N/m2

After substituting the values we get,

f178.2Hz



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