Two sounds having the same speed in a medium are having wavelengths 1.3 m and 3.9 m. A person listens to these sounds. What is the difference between the two sounds the person hears?

Second sound is louder

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First sound is heard with higher pitch

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Second sound is heard with better clarity

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First sound is heard with better quality

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Solution

The correct option is B
First sound is heard with higher pitch

Since velocity (v) is the product of frequency (f) and wavelength (w),
$f_{1}$ = $\frac{v}{w_{1}}$ = $\frac{v}{1.3}$ = $\frac{10 v}{13}$ = $\frac{30 v}{39}$
$f_{2}$ = $\frac{v}{w_{2}}$ = $\frac{v}{3.9}$ = $\frac{10 v}{39}$
Now, $\frac{f_{1}}{f_{2}}$ = $\frac{\frac{30 v}{39}}{\frac{10 v}{39}}$ = 3
As $f_{1}$ is 3 times greater than $f_{2}$ , first sound has higher pitch than the second one, because higher the frequency, higher is the pitch.

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