Question

The length of a sonometer wire is $0.75\, m$ 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)

$I=0.75 \,m \,\,\,\rho=9 \times 10^{3} Kg / m ^{3}$
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 $=\frac{v}{2 l}$
$=\frac{300}{2 \times 0.75}=200 \,Hz$