Question

Two trains A and B approach a stationary observer from opposite sides as shown in the figure. Observer hears no beats. If frequency of the horn of train B is 504 Hz, the frequency of horn of train A is : (approximately) (velocity of sound = 330 m/s)

• A. 504 Hz
• B. 529 Hz
• C. 526 Hz
• D. 462 Hz

Answer 1

Answer: (B)

529 Hz

Velocity of train B is $V_B=30m/s$
Original frequency of train B $f_B=504Hz$
Thus apparent frequency of B heard by observer,
$f_B^{\prime }=f_B[\frac{V_{sound}}{V_{sound}-V_B}]$
$\therefore$ $f_B^{\prime }=504[\frac{330}{330-30}]=554.4Hz$
Velocity of train A is $V_A=15m/s$
Let the original frequency of train A be $f_A$.
Thus apparent frequency of A heard by observer,
$f_A^{\prime }=f_A[\frac{V_{sound}}{V_{sound}-V_A}]$
$\therefore$ $f_A^{\prime }=f_A[\frac{330}{330-15}]=1.047f_{A}Hz$
Since the observer hears no beats, so $f_A^{\prime }=f_B^{\prime }$
$\therefore$ $1.047f_A=554.4$
$⟹f_A=529Hz$