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)

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