Question

A girl swings in a cradle with period $\pi /4$ second and amplitude 2m. A boy standing infront of it blows a whistle of natural frequency 1000 Hz. The minimum frequency as heard by the girl is: (Velocity of sound in air is 320 ms${}^{-1}$)

• A. 850 Hz
• B. 1000 Hz
• C. 750 Hz
• D. 950 Hz

Answer 1

The correct option is D 950 Hz

Maximum velocity, $v=A\omega$ $=2\left(\frac{2\pi }{\frac{\pi }{4}}\right)=16m$
Minimum frequency occurs at other extreme, i.e person moving away
$\therefore f^{\prime }=\left(\frac{v-v_o}{v}\right)f$

$=\left(\frac{320-20}{320}\right)\times 1000$

$=\frac{15}{16}\times 1000=950Hz$