Wave Mechanics Question 654
Question: A sonometer wire of length 1.5 m 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\times 10^{3}kg/m^{3} $ and $ 2.2\times 10^{11}N/m^{2} $ respectively?
Options:
A) 188.5 Hz
B) 178.2 Hz
C) 200.5 Hz
D) 770 Hz
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Fundamental frequency, $ f=\frac{v}{2\ell }=\frac{1}{2\ell }\sqrt{\frac{T}{\mu }}=\frac{1}{2\ell }\sqrt{\frac{T}{A\rho }} $
$ ,[ \because v=\sqrt{\frac{T}{\mu }},and,\mu =\frac{m}{\ell } ] $ Also, $ Y=\frac{T\ell }{A\Delta \ell }\Rightarrow \frac{T}{A}=\frac{Y\Delta \ell }{\ell } $
$ \Rightarrow ,f=\frac{1}{2\ell }\sqrt{\frac{\gamma \Delta \ell }{\ell \rho }} $ ? (i) Putting the value of $ \ell ,,\frac{\Delta \ell }{\ell } $ , $ \rho $ and $ \gamma $ in $ eq^{n} $ . (i) we get, $ f=\sqrt{\frac{2}{7}}\times \frac{10^{3}}{3} $ or, $ f\approx 178.2Hz $
BETA
