Question

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

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

Answer 1

The correct option is D $20\%$ decrease

We know that:

$v=f\lambda$
Since, the medium has not changed, speed of wave remains same.
$v=f\lambda =$ constant
$f_1{\lambda }_1=f_2{\lambda }_2$
$f_1{\lambda }_1=\left(1.25f_1\right){\lambda }_2$
$(\because$ frequency increased by $25\%)$
${\lambda }_2=\frac{{\lambda }_1}{1.25}$
${\lambda }_2$ decreases.
Now $,\%$ change in wavelength
$\frac{{\lambda }_1-{\lambda }_2}{{\lambda }_1}\times 100$
$\frac{{\lambda }_1-\frac{{\lambda }_1}{1.25}}{{\lambda }_1}\times 100$
$\frac{0.25}{1.25}\times 100$
$\frac{100}{5}\times 20\%$

Final answer: $\left(b\right)$