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Question
Figure shows a plot of the transverse displacements of the particles of a string at t = 0 through which a travelling wave is passing in the positive x-direction. The wave speed is 20 cm s−1. Find (a) the amplitude, (b) the wavelength, (c) the wave number and (d) the frequency of the wave.
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Solution
Given:
Wave speed,
ν = 20 cm/s
From the graph, we can infer:
(a) Amplitude, A = 1 mm
(b) Wavelength, λ = 4 cm
(c) Wave number,
\[k = \frac{2\pi}{\lambda}\]
\[= \frac{\left( 2 \times 3 . 14 \right)}{4}\]
\[ = 1 . 57 {cm}^{- 2} \]
(d) Time Period , T = \[\frac{\lambda}{\nu}\]
\[\text{ Frequency, f } = \frac{1}{T} = \frac{v}{\lambda}\]
\[ \Rightarrow f = \frac{20}{4} = 5 Hz\]
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