Question

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

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

Answer 1

Answer: (D)

Given, frequency of oscillating tuning fork $(n)=170\, Hz$
Speed of tuning fork $\left(v_{0}\right)=2\, ms ^{-1}$
Velocity of sound $(v)=340\, ms ^{-1}$
We know that,
$n^{'}=\left(\frac{v+v_{0}}{v-v_{0}}\right) n $
or$n^{'}=\left(\frac{340+2}{340-2}\right) \times 170$
or,$n^{'}=\frac{342}{338} \times 170$
or, $n^{'}=172.01 \approx 172 \, Hz$
The beat frequency observed by the student between fork and its echo is
$(172-170)=2\, Hz $