Question

In a sonometer a stretched wire is observed to vibrate with a frequency of $30Hz$ in the fundamental mode, when the distance between bridges is $0.6m$. If the string has a linear mass of $0.05kg{m}^{-1}$ then the velocity of propagation of transverse wave in the string and the tension in the string are

• A. $36m/s,64.8N$
• B. $46m/s,64.8N$
• C. $54m/s,64.8N$
• D. $36m/s,54.8N$

Answer 1

The correct option is A $36m/s,64.8N$

Fundamental frequency, $\left(f\right)=\frac{v}{2L}$
$30=\frac{v}{2\left(0.6\right)}$

$v=30\times 2\times 0.6$ $=36m/s$

$v=\sqrt{\frac{T}{linearmass}}$

$36=\sqrt{\frac{T}{0.05}}$

$T=36\times 36\times 0.05$ $=64.8N$