First slide

Stationary waves

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 $7.7 \times 10^{3} k g / m^{2}$ and $2.2 \times 10^{11} N / m^{2}$ respectively ?

Moderate

A

188.5 Hz
B

178.2 Hz
C

200.5 Hz
D

770 Hz

Solution

$F u n d a m e n t a l f r e q u e n c y f = \frac{1}{2 l} \sqrt{\frac{T}{μ}} = \frac{1}{2 l} \sqrt{\frac{T}{m / l}} = \frac{1}{2 l} \sqrt{\frac{T}{m / l}} = \frac{1}{2 l} \sqrt{\frac{\frac{T}{A}}{\frac{m}{A l}}} = \frac{1}{2 l} \sqrt{\frac{s t r e s s}{ρ}} \Rightarrow f = \frac{1}{2 l} \sqrt{\frac{Y \times s t r a i n}{ρ}} \Rightarrow f = \frac{1}{2 \times 1.5} \sqrt{\frac{2.2 \times 10^{11} \times 1}{7.7 \times 10^{3} \times 100}} \Rightarrow f = 178.17 H z$

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