Question

A sonometer wire having a length of $1.50m$between the bridges vibrates in its second harmonic in resonance with a tuning fork of frequency $256Hz$. What is the speed of the transverse wave on the wire?

Answer 1

Step 1 : Given data

Length of the sonometer wire $L=1.50m$

Frequency of tuning fork $f=256Hz$

Step 2 : To find the speed of transverse wave

Let the first harmonic be $f_0$ and the second harmonic be $f_1$ , $f_1=256Hz$

First harmonic for fundamental frequency ,

$$\begin{gathered} f_0=\frac{f_1}{2} \\ =\frac{256}{2} \\ =128Hz \end{gathered}$$

$$\begin{gathered} \frac{\lambda }{2}=1.5m \\ \lambda =1.5\times 2 \\ =3m \end{gathered}$$

Wave speed $$\begin{gathered} v=f_0\lambda \\ v=128\times 3=384m{s}^{-1} \end{gathered}$$

Hence the speed of transverse wave $=384m{s}^{-1}$