Question

The wavelength of a sound wave is reduced by 50%. Then the percentage change in its frequency will be

• A. 100%
• B. 200%
• C. 400%
• D. 800%

Answer 1

Answer: (A)

100%

The wavelength of sound wave is

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

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

where, v is the velocity of sound waves and $\nu$ is the frequency of sound waves.

When the wavelength of a sound wave is reduced by 50%

$\lambda -\frac{50}{100}\lambda =\frac{v}{{\nu }^{\prime }}$

$\frac{1}{2}\lambda =\frac{v}{{\nu }^{\prime }}$

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

The percent change in frequency is

$\frac{\nu -{\nu }^{\prime }}{\nu }\times 100=\frac{\frac{2v}{\lambda }-\frac{v}{\lambda }}{\frac{v}{\lambda }}\times 100$

$\Rightarrow (2-1)\times 100=100$%