Question

Sound waves of wavelength $\lambda$ travelling in a medium with a speed of $vm/s$ enter into another medium where its speed is $2vm/s$. Wavelength of sound waves in the second medium is

• A. $\lambda$
• B. $2\lambda$
• C. $4\lambda$
• D. $\lambda /2$

Answer 1

The correct option is B $2\lambda$

As the frequency is given by,

$\nu =\frac{v}{\lambda }$

$\Rightarrow \lambda =v/\nu$ …(i)

Where, $v=$Speed of light,

$\lambda =$Wavelength of the wave

Let, ${\nu }_1=$Frequency in first medium

${\nu }_2=$Frequency in second medium

${\lambda }_1=$Wavelength in first medium$=\lambda$

${\lambda }_2=$Wavelength in second medium

$v_1=$Speed in first medium$=v$

$v_2=$Speed in second medium$=2v$

As the frequency remains unchanged in both mediums.

So, from equation (i)

$\lambda =\left(\frac{2v}{v}\right){\lambda }_1=2{\lambda }_1$

Hence the wavelength of sound waves in the second medium is $2\lambda$.

Final Answer: (c)