Question

Two sounds in a medium are having wavelengths $1.3m$ and $3.9m$. A person listens to these sounds. What difference would the listener feel?

• A. First sound is heard with higher pitch.
• B. First sound is heard with better quality.
• C. First sound is louder.
• D. Second sound is heard with higher pitch.

Answer 1

The correct option is A

First sound is heard with higher pitch.

Given:
Medium is the same for both the sounds.
For first sound, wavelength ${\lambda }_1=1.3m$
For second sound, wavelength ${\lambda }_2=3.9m$

Speed of sound in a medium is constant.
Since velocity (v) is the product of frequency (f) and wavelength $\left(\lambda \right)$,
$f_1=\frac{v}{{\lambda }_1}$
$f_2=\frac{v}{{\lambda }_2}$

$⟹\frac{f_1}{f_2}=\frac{{\lambda }_2}{{\lambda }_1}$
$\frac{f_1}{f_2}=\frac{3.9}{1.3}$
$f_1=3f_2$

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.