Question

The given graph shows the displacement versus time relation for a disturbance travelling with velocity of $1500\text{m/s}$. Calculate the wavelength of the disturbance.

Answer 1

Given -
Velocity $\left(v\right)=1500\text{m/s}$
To find - Wavelength $\left(\lambda \right)$ of the sound wave

Time period $\left(T\right)$ of $1$ oscillation
$=2\mu \text{s}=2\times {10}^{(-6)}\text{s}$
Now, Frequency $\left(\nu \right)=1/\text{Time period}\left(T\right)$
$=1/(2\times {10}^{(-6)}\text{s})$

$\nu =5\times {10}^5\text{Hz}$
Speed of sound wave $\left(C\right)$ is given by,
$c=\nu \times \lambda$
$1500=5\times {10}^5\times \lambda$
or $\lambda =3\times {10}^{(-3)}\text{m}$
Hence wavelength of the disturbance is
$3\times {10}^{(-3)}\text{m}$.