Question

If the frequency of a sound wave is increased by 25%, then the change in its wavelength will be

• A. 25% decrease
• B. 20% decrease
• C. 20% increase
• D. 25% increase

Answer 1

Answer: (B)

20% decrease

The frequency of wave is given by

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

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

When the frequency of a sound wave is increased by 25%, then the new

wavelength is

${\lambda }^{\prime }=\frac{v}{\nu +\frac{25}{100}\nu }$

${\lambda }^{\prime }=\frac{v}{\nu +\frac{1}{4}\nu }$

${\lambda }^{\prime }=\frac{v}{\frac{5}{4}\nu }$

${\lambda }^{\prime }=\frac{4v}{5\nu }$

Hence, the percent change in wavelength is

$\frac{\lambda -{\lambda }^{\prime }}{\lambda }\times 100=\frac{\frac{v}{\nu }-\frac{4v}{5\nu }}{\frac{v}{\nu }}\times 100$

$\Rightarrow -\frac{1}{4}\times 100=-20$%.

Hence, wavelength decreases by 20%