The length of a sonometer wire is 0.75m and density is 9×103kg/m3. It can bear a stress of 8.1×108N/m2 without exceeding elastic limit. The fundamental frequency that can be produced in the wire is
A
200Hz
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B
150Hz
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C
175Hz
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D
225Hz
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Solution
The correct option is A200Hz Given, l=0.75m,ρ=9×103kg/m3 σ=8.1×108N/m2
Let the cross-sectional area be A.
Tension, T= Stress × Area ⇒T=8.1×108A
Linear mass density, μ=ρA=9×103A
Now, speed of the wave, v=√Tμ ⇒v=√8.1×108A9×103A ⇒v=300m/s
So, fundamental frequency, f0=v2l=3002×0.75 ⇒f0=200Hz