Question

Standing waves are produced in a string by sources at each end with a frequency of 10.0 Hz. The distance between the third and sixth node is 54 cm.A. What is the wavelength of the interfering waves?B. What is the speed of the waves?

Answer 1

Given that the frequency is f = 10 Hz

The distance between the third and sixth nodes is 54 cm.

(A) The points are the nodes, The difference between the third and sixth nodes is one and a half wavelength, so

$\begin{gathered} \lambda+\frac{\lambda}{2}=54 \\ \frac{3\lambda}{2}=54\text{ cm} \\ \lambda=36\text{ cm} \\ =0.36\text{ m} \end{gathered}$

(B) Speed of the wave is

$\begin{gathered} v=\lambda\times f \\ =3.6\text{ m/s} \end{gathered}$