Question

A person $B$ accidentally slips from a large building and screams with a sound of constant frequency $n$ as he falls as shown in the figure. The apparent frequency of the sound of the scream as heard by the person $A$, at the top of the building is dependent on time as ($v$ is speed of sound)

• A. $n^{\prime }=n\left(\frac{v}{v-gt}\right)$
• B. $n^{\prime }=n\left(\frac{v}{v+gt}\right)$
• C. $n^{\prime }=n\left(\frac{2v}{2v+g{t}^2}\right)$
• D. $n^{\prime }=n\left(\frac{2v}{2v-g{t}^2}\right)$

Answer 1

Answer: (B)

The person $B$ moves away from person $A$
or the source of sound moves away from $A$.
Hence, the apparent frequency is
$n^{\prime }=n\left(\frac{v}{v+v_s}\right)$
where $v_s$ is the speed of sound and $v_B$ is the speed of the person B(source)
Since $($ from $v=u+at$ and $u=0$ )
$v_S=gt$
we get, $n^{\prime }=n\left(\frac{v}{v+gt}\right)$