Question

Figure (15-E2) 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.

Answer 1

Given:
Wave speed, $\nu =20\mathrm{cm}/\mathrm{s}$
From the graph, we can infer:
(a) Amplitude, A = 1 mm
(b) Wavelength, λ = 4 cm

(c) Wave number, $k=\frac{2\pi }{\lambda }$
$$\begin{gathered} =\frac{\left(2\times 3.14\right)}{4} \\ =1.57{\mathrm{cm}}^{-2} \end{gathered}$$

(d) $\mathrm{Time}\mathrm{period},\mathit{}T=\frac{\lambda }{\nu }$
$$\begin{gathered} \mathrm{Frequency},f=\frac{1}{T}=\frac{v}{\lambda } \\ \Rightarrow f=\frac{20}{4}=5\mathrm{Hz} \end{gathered}$$