Question

A sonometer wire having a length of 1⋅50 m between the bridges vibrates in its second harmonic in resonance with a tuning fork of frequency 256 Hz. What is the speed of the transverse wave on the wire?

Answer 1

Wave Speed is 384 m/s

Explanation:

Given:

Length of the sonometer wire (L) = 1.50 m

Let the first harmonic be $f_0$ and the second harmonic be $f_1$

According to the question, $f_1$ = 256 Hz

1st harmonic for fundamental frequency, $f_0 = \frac {f_1}{2} = \frac {256}{2}$

= 128 Hz

When the fundamental wave is produced, we have:

$\frac {\lambda}{2}$ = 1.5 m

So, $\lambda$ = 3 m

Wave Speed, v = $f_0 \lambda$

or v = $128 \times 3$ = 384 $ms^-^1$