Question

Sound waves of wavelength $\lambda$ travelling in a medium with a speed of $vm{s}^{-1}$ enter into another medium where its speed is $2vm{s}^{-1}$. 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)

$2\lambda$

Wavelength of sound waves in the first medium,

$\lambda =\frac{v}{\nu }$ .......(i)

Wavelength of sound waves in the second medium,

${\lambda }^{\prime }=\frac{2v}{{\nu }^{\prime }}$ ........(ii)

As the frequency of the wave remains unchanged with the change in medium

$\therefore \nu ={\nu }^{\prime }$ .........(iii)

Divide (ii) by (i), we get

$\frac{{\lambda }^{\prime }}{\lambda }=2$

or ${\lambda }^{\prime }=2\lambda$