Question

A student holds a tuning fork oscillating at $170Hz$. He walks towards a wall at a constant speed of $2m{s}^{-1}$. The beat frequency observed by the student between the tuning fork and its echo is
(Velocity of sound $=340m{s}^{-1}$ )

• A. 2.5 Hz
• B. 3 Hz
• C. 1 Hz
• D. 2 Hz

Answer 1

Answer: (D)

Given, frequency of oscillating tuning fork $(n)=170Hz$
Speed of tuning fork $\left(v_0\right)=2m{s}^{-1}$
Velocity of sound $(v)=340m{s}^{-1}$
We know that,
$n^{{}^{\prime }}=\left(\frac{v+v_0}{v-v_0}\right)n$
or$n^{{}^{\prime }}=\left(\frac{340+2}{340-2}\right)\times 170$
or,$n^{{}^{\prime }}=\frac{342}{338}\times 170$
or, $n^{{}^{\prime }}=172.01\approx 172Hz$
The beat frequency observed by the student between fork and its echo is
$(172-170)=2Hz$