Question

The figure showed the shape of part of a long string in which transverse waves are produced by attaching one end of the string to the tuning fork of frequency 250Hz. What is the velocity of the waves?

(A) 1.0 ms$^{-1}$
(B) 1.5 ms$^{-1}$
(C) 2.0 ms$^{-1}$
(D) 2.5 ms$^{-1}$

Answer 1

Hint: The product of frequency of a wave multiplied by the wavelength of the wave gives the velocity of the wave. The velocity is also called phase velocity as it is with this velocity that a particle performs SHM in a transverse wave on its position.
Formula used:
The product of frequency and wavelength gives the velocity of the wave:
$v = f \lambda$

Complete answer:
The frequency of a wave is defined as the number of waves that cross a given distance per unit time, in other words, number of complete cycles being executed per unit time. We are given that the wave on the string has a frequency of 250 Hz.
The given wave forms on a long string. We are given the amplitude in centimetre and wavelength in centimetres. Wavelength of a wave is defined as the distance between two crests or troughs.
The wavelength of the given wave can be obtained by checking the distance between two crests (or troughs) from the given figure. We can see from the figure that the distance can be obtained as:
$\lambda = 0.5 - 0.1 = 0.4$ cm.
The velocity is obtained:
$v = f \lambda = 250 \text{Hz} \times 0.004 \text{m} = 1.0 ms^{-1}$.

Therefore the correct answer is option (A).

Note:
The graph given is a picture of vibrations of string therefore, the picture is in centimetre both along the x and the y axis. Whenever a picture of a wave comes up, one has to carefully note the x and y coordinates. There are also graphs given that depict time and amplitude relation. In some other graphs that denote the electromagnetic waves, the amplitude has units of V/m in case of electric fields for example.