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The MCQs below are drawn from the Physics subject category.
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951
A car is moving with a velocity of 30 m s^-1 towards a high wall. If frequency of siren of car is 600 Hz and velocity of sound is 330 m s^-1, then the apparent frequency of the echo of siren will be:
The reflected wave experiences two Doppler shifts: f' = f (v+u)/(v-u). With v=330 m/s and u=30 m/s, f' = 600*(360/300)=720 Hz.
952
A racing car moving towards a cliff sounds its horn. The driver observes that the sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If v is the velocity of sound, then the velocity of the car is?
An open-open pipe supports standing waves with both even and odd harmonics, so it contains all harmonics.
955
A man is watching two trains, one leaving and the other coming in with equal speeds of 4 m/sec. If they sound their whistles, each of frequency 240 Hz, the number of beats heard by the man (velocity of sound in air = 320 m/sec) is
The OCR marks 'Stationary longitudinal waves'; resonating air columns form standing (stationary) longitudinal waves.
958
A tuning fork of frequency 480 Hz produces 10 beats/sec when sounded with a sonometer string. A slight increase in tension in the sonometer string produces fewer beats/sec than before. What was the frequency of the sonometer string?
Initial beat frequency |480 − f| = 10 so f = 470 or 490. Increasing tension raises f; fewer beats implies f moved closer to 480, so initial f = 470 Hz.
959
A man is watching two trains, one leaving and the other coming with equal speeds of 4 m s^-1. The trains sound their whistles each of natural frequency 240 Hz. If velocity of sound in air is 320 m s^-1, then the number of beats heard by the man is
Approaching frequency ≈ 240×(320/316) ≈243.04 Hz and receding ≈240×(320/324) ≈237.04 Hz, difference ≈6 Hz, so about 6 beats per second.
960
A vibrating sonometer wire produces 4 beats per second with a tuning fork when its length is either 60 cm or 61 cm. The frequency of the tuning fork must be
Frequency ∝ 1/length; the frequency difference between the two wire lengths equals 8 Hz (twice the beat frequency if fork lies between them), giving a fork frequency ≈ 484 Hz.