Question

The length of a sonometer wire is $0.75m$ and density $9\times 10^{3}Kg/m^3$. It can bear a stress of $8.1\times 10^{8}N/m^2$ without exceeding the elastic limit. The fundamental frequency that can be produced in the wire, is

• A. 200 Hz
• B. 150 Hz
• C. 600 Hz
• D. 450 Hz

Answer 1

Answer: (A)

$I=0.75m\rho =9\times 10^{3}Kg/m^3$
Limiting stress $=8.1\times 10^{8}N/m^2$
Let area be equal to $A$.
Tension $(T)=\text{ Stress }\times \text{ Area }$
$=8.1\times 10^8\times A$
Mass $/$ length $(\mu )=\rho A$
Velocity $(v)=\sqrt{\frac{T}{\mu }}=\frac{8.1\times 10^8\times A}{9\times 10^3\times A}$
$=\sqrt{\frac{8.1\times 10^5}{9}}$
$=\sqrt{9\times 10^4}=3\times 10^{2}m/s$
Maximum fundamental frequency $=\frac{v}{2l}$
$=\frac{300}{2\times 0.75}=200Hz$