Question

Sound waves of wavelength $\lambda$ travelling in a medium with a speed of $v\, m\, s^{-1}$ enter into another medium where its speed is $2v\, m\, s^{-1}$. Wavelength of sound waves in the second medium is

• A. $\lambda$
• B. $\frac{\lambda}{2}$
• C. $2\lambda$
• D. $4\lambda$

Answer 1

Answer: (C)

Wavelength of sound waves in the first medium,
$\lambda = \frac{v}{\upsilon} \quad...(i)$
Wavelength of sound waves in the second medium
$ \lambda' = \frac{v}{\upsilon'}\quad ...(ii)$
As the frequency of the wave remains unchanged with the change in medium
$\therefore \upsilon= \upsilon' \quad...\left(iii\right)$
Divide $(ii)$ by $(i)$, we get
$\frac{\lambda'}{\lambda} = 2$ [Using $(iii)$]
or $\lambda ' = 2\lambda$