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

The correct option is B 20 % decrease

Since, the medium has not changed, speed of wave remains
same.
$v={\nu }_1{\lambda }_1={\nu }_2{\lambda }_2$
${\nu }_2=1.25{\nu }_1$
${\lambda }_2=\frac{{\nu }_1}{{\nu }_2}{\lambda }_1=\frac{1}{1.25}{\lambda }_1=\left(4/5\right){\lambda }_1$
$\frac{\Delta \lambda }{{\lambda }_1}=\frac{{\lambda }_2-{\lambda }_1}{{\lambda }_1}\times 100=\frac{\left(4/5\right){\lambda }_1-{\lambda }_1}{{\lambda }_1}\times 100=-\left(1/5\right)\times 100=-20$ %
option "B" is correct.