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 $20cm{s}^{-1}$. Find $\left(a\right)$ the amplitude, $\left(b\right)$ the wavelength, $\left(c\right)$ the wave number and $\left(d\right)$ the frequency of the wave.

Answer 1

Step 1. Given data

Given, $V=20cm{s}^{-1}$

Step 2. Calculating amplitude, wavelength, wavenumber, frequency

From the given figure,

The amplitude is $A=1mm$

The wavelength is $\lambda =4cm$

The wave number is given as

$$\begin{gathered} n=\frac{2\pi }{\lambda } \\ n=\frac{2\times 3.14}{4} \\ n=1.57c{m}^{-1} \end{gathered}$$

The frequency is

$$\begin{gathered} f=\frac{1}{T} \\ f=\frac{20}{4} \\ f=5Hz \end{gathered}$$ where, $T=\frac{\lambda }{V}$

Hence, the amplitude is $1mm$, wavelength is $4cm$, wavenumber is $1.57c{m}^{-1}$ and frequency is $5Hz$.