Question

If the speed of a transverse wave on a stretched string of length $1m$ is $60m{s}^{-1}$, what is the fundamental frequency of vibration?

Answer 1

Step 1: Given data

A speed of the stretched string of length $1m$ is $60m/s$.

Step 2: Diagram:

Step 3: Formula Used:

For the fundamental mode of a stretched string as shown

$$\begin{gathered} L=\lambda /2 \\ \lambda =2L \\ {v}_0=\frac{v}{\lambda } \end{gathered}$$

where, L is the length of the string, $\lambda$ is the wavelength, $v_0$ is the fundamental frequency of vibration, $v$ is the speed of the transverse wave.

Step 4: Calculation:

$$\begin{gathered} v_0=\frac{v}{\lambda } \\ =\frac{v}{2L} \\ =\frac{60}{2} \\ =30Hz \end{gathered}$$

Hence, the fundamental frequency of vibration is $30Hz$.