Question

A string of mass $0.2kg/m$ in length $L=0.6m$ is fixed at both ends and stretched such that it has a tension of $80N.$ The string is vibrating in its third normal mode, has an amplitude of $0.5cm$. What is the frequency of oscillation? What is the maximum transverse velocity amplitude?

• A. $50Hz,50\pi cm/sec.$
• B. $20Hz,50\pi cm/sec.$
• C. $50Hz,20\pi cm/sec.$
• D. $100Hz,50\pi cm/sec.$

Answer 1

The correct option is A $50Hz,50\pi cm/sec.$

Frequency of vibrating in third normal mode=$\nu =\frac{3}{2L}\sqrt{\frac{T}{\mu }}$

$=\frac{3}{2\times 0.6}\sqrt{\frac{80}{0.2}}=50Hz$

Maximum transverse amplitude velocity is given as $\omega A$

$=2\pi \nu A=50\pi cm/s$