Question

If the frequency of a wave is increased by $25\%$ in the same medium. The change in its wavelength will be

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

Answer 1

The correct option is B decrease of $20\%$

Here, medium is not changed, hence
speed $\left(v\right)$ of the wave will remain the same.
$\Rightarrow v=$ constant
$\Rightarrow f\lambda =$ constant
$\Rightarrow f_1{\lambda }_1=f_2{\lambda }_2$
$f$ is increased by $25\%$, hence, $f_2=1.25f_1$
So,
$f_1{\lambda }_1=\left(1.25f_1\right){\lambda }_2$
$\Rightarrow {\lambda }_2=\frac{f_1{\lambda }_1}{1.25f_1}$
$\Rightarrow {\lambda }_2=\frac{{\lambda }_1}{1.25}=0.8{\lambda }_1$
$\%$ change in wavelength,
$\%\Delta \lambda =\frac{{\lambda }_2-{\lambda }_1}{{\lambda }_1}\times 100$
$\Rightarrow \%\Delta \lambda =\frac{0.8{\lambda }_1-{\lambda }_1}{{\lambda }_1}\times 100$
$\Rightarrow \%\Delta \lambda =-20\%$
Wavelength will get decreased by $20\%$.