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
$f_1{\lambda }_1=f_2{\lambda }_2$
$\Rightarrow f_1{\lambda }_1=\left(1.25f_1\right){\lambda }_2$ ($\because$ frequency increased by $25\%$ )
${\lambda }_2=\frac{{\lambda }_1}{1.25}\Rightarrow {\lambda }_2$ decreases.
$\%$ change in wavelength
$=\frac{{\lambda }_1-{\lambda }_2}{{\lambda }_1}\times 100$
$\frac{{\lambda }_1-\frac{{\lambda }_1}{1.25}}{{\lambda }_1}\times 100$
$=\frac{0.25}{1.25}\times 100=\frac{100}{5}=20\%$