First slide

Characterstics of wave

Question

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

Moderate

A

20% increase
B

20% decrease
C

25% increase
D

25% decrease

Solution

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

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