Question

The given graph shows the displacement versus time relation for a disturbance travelling with velocity of 1500 ms−1 . Calculate the wavelength of the disturbance.

Answer 1

Step 1: Given data

Wave speed,$v=1500m{s}^{-1}$

From the graph, we can see that,

Time period,$T=2\times {10}^{-6}s$

Step 2: Finding the frequency of the wave

The formula for frequency is $f=\frac{1}{T}$

$f=\frac{1}{T}=\frac{1}{2\times 10{}^{-6}s}$.

Step 3: Finding the speed of the wave

Wave speed v,

$$\begin{gathered} v=f\lambda \\ \lambda =\frac{v}{f}=\frac{1500}{\left({\displaystyle \frac{1}{2\times {10}^{-6}}}\right)}=1500\times 2\times {10}^{-6} \end{gathered}$$

$\Rightarrow \lambda =3\times {10}^{-3}m.$

Thus, the wavelength of the transmitted wave is $3\times {10}^{-3}m.$