Question

On a platform a man is watching two trains one leaving the station the other approaching the station, both with the same velocity $2$ m/s and blowing their horn with a frequency $480$ Hz. The number of beats heard by the man will be (Velocity of sound in air is $320$ m/s)

• A. $6$
• B. $3$
• C. $2$
• D. $4$

Answer 1

The correct option is A $6$

Frequency of sound heard by man from approaching trains

[A]

$\begin{array}{cc}{n}_a=n\left(\frac{V}{V-V_5}\right),& \begin{array}{c}V=Speedofsound\\ V_5=Speedoftrain\end{array}\\ =480\left(\frac{320}{320-2}\right)& n=frequencyofhorn\\ n_a=483Hz& \end{array}$

Frequency of sound heard from receding train

$n_r=n\left(\frac{V}{V-V_5}\right)=480\left(\frac{320}{322}\right)=477Hz$

$\therefore$ number of heats heard = $n_a-n_r=483-477=6$