Question

If the frequency of a wave is increased by $25 \%$, then the change in its wavelength will be: (medium not changed)

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

Answer 1

Answer: (B)

Since, the medium has not changed, speed of wave remains same.
$\Rightarrow v=f \lambda=$ constant
$f_{1} \lambda_{1}=f_{2} \lambda_{2}$
$\Rightarrow f_{1} \lambda_{1}=\left(1.25 f_{1}\right) \lambda_{2}$ ($\because$ frequency increased by $25 \%$ )
$\lambda_{2}=\frac{\lambda_{1}}{1.25} \Rightarrow \lambda_{2}$ decreases.
$\%$ change in wavelength
$=\frac{\lambda_{1}-\lambda_{2}}{\lambda_{1}} \times 100$
$\frac{\lambda_{1}-\frac{\lambda_{1}}{1.25}}{\lambda_{1}} \times 100$
$=\frac{0.25}{1.25} \times 100=\frac{100}{5}=20 \%$