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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%
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B
decrease of 20%
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C
increase of 25%
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D
decrease of 25%
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Solution

The correct option is B decrease of 20%
Here, medium is not changed,
hence,
speed (v) of the wave will remain the same.
v= constant
fλ= constant
f1λ1=f2λ2
f is increased by 25%, hence, f2=1.25f1
So,
f1λ1=(1.25f1)λ2
λ2=f1λ11.25f1
λ2=λ11.25=0.8λ1
% change in wavelength,
%Δλ=λ2λ1λ1×100
%Δλ=0.8λ1λ1λ1×100
%Δλ=20%
Wavelength will get decreased by 20%.

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