JEE PYQ: Waves And Sound Question 39
Question 39 - 2019 (09 Jan Shift 2)
A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to:
(1) 666 Hz
(2) 753 Hz
(3) 500 Hz
(4) 333 Hz
Show Answer
Answer: (1)
Solution
Frequency of the sound produced by open flute:
$f = 2\left(\frac{v}{2l}\right) = \frac{2 \times 330}{2 \times 0.5} = 660$ Hz
Velocity of observer, $v_0 = 10 \times \frac{5}{18} = \frac{25}{9}$ m/s
As the source is moving towards the observer therefore, according to Doppler’s effect:
$\therefore$ Frequency detected by observer,
$f’ = \left(\frac{\frac{25}{9} + 330}{330}\right) f = \frac{2995}{9 \times 330} \times 660$
$f’ = 665.55$ or, $f’ \approx 666$ Hz
BETA
