Question

A steel wire $0.5$ metre long and of mass $5\times {10}^{-3}kg$ is stretched with a tension $400N$. What is the number of highest overtone that could be heard by a person who can hear frequencies up to $10kHz$?

• A. $39$
• B. $49$
• C. $29$
• D. $19$

Answer 1

The correct option is B $49$

Length of wire$=0.5m$
Mass of wire$=5\times {10}^{-3}kg$
Linear density$=0.01kg{m}^{-1}$
Tension$=400N$
fundamental frequency$=\frac{1}{2L}\sqrt{\frac{T}{M}}=\frac{1}{2\times 0.5}\sqrt{\frac{400}{0.01}}$
$=200Hz$
Highest harmonic the person can hear$=\frac{10kHz}{200}=50$
Highest number of overtone that can be heard$=49$