Question

A wave of frequency 100 Hz travels along a string towards its fixed end. When this wave travels back, after reflection, a node is formed at a distance of 10 cm from the fixed end. The speed of the wave (incident and reflected) is
(A) 20 m/s
(B) 40 m/s
(C) 5 m/s
(D) 10 m/s

Answer 1

This is an example of the problem wave on a string. Given the frequency of the wave which remains unchanged. Wave is reflected and reflection a node is formed. We know when a stationary wave is produced the fixed ends behave as a node.

Complete step by step answer:
F= 100 Hz
Node is formed at 10 cm,
=0.1 m
The wavelength can be found as= $2\times 0.1=0.2m$
Now after finding the wavelength we need to find the speed of the wave. We know the relationship between velocity, wavelength and frequency is given by $v=f\lambda$
= $100\times 0.2=20m/s$
So, the velocity of the wave is 20 m/s. thus, the correct option is (A),
Additional Information:
Standing waves are produced when waves travel in diametrically opposite directions. Nodes and antinodes are a region where there are no vibrations. The points in a standing wave that appear to remain flat and do not move are called nodes

Note: The relationship between velocity, wavelength and frequency is given by $v=f\lambda$.In this the frequency is the characteristic of the source which is producing the wave and it remains constant during propagation. The velocity and wavelength changes during the propagation of the wave.