Sound waves of wavelength $\mathrm{\lambda }$ travelling in a medium with a speed of v m/s enter into another medium where its speed is 2v m/s. The wavelength of sound waves in the second medium is:

1. $\mathrm{\lambda }$

2. $\frac{\mathrm{\lambda }}{2}$

3. $2\mathrm{\lambda }$

4. $4\mathrm{\lambda }$

(3) Hint: The frequency of the wave remains the same.
Step 1: Find the wavelength of the wave in the second medium.
Let the frequency in the first medium is $\mathrm{\nu }$ and in the second medium is $\mathrm{\nu }\text{'}$.
Frequency remains the same in both the medium.
So,                                                     $\nu \mathit{=}\nu \mathit{\text{'}}⇒\frac{\mathrm{v}}{\mathrm{\lambda }}=\frac{\mathrm{v}\text{'}}{\mathrm{\lambda }\text{'}}$
$⇒$                                                     $\mathrm{\lambda }\text{'}=\left(\frac{\mathrm{v}\text{'}}{\mathrm{v}}\right)\mathrm{\lambda }$
And v and v' are speeds in the first and second medium respectively.
So,                                                  $\mathrm{\lambda }\text{'}=\left(\frac{2\mathrm{v}}{\mathrm{v}}\right)\mathrm{\lambda }=2\mathrm{\lambda }$