Sound(12th Grade > Physics ) Questions and answers for exam Preparation

12th Grade > Physics

SOUND MCQs

Total Questions : 31 | Page 2 of 4 pages

Question 11. Two sound sources are moving in opposite directions with velocities

v_{1}

and

v_{2} (v_{1} > v_{2})

. Both are moving away from a stationary observer. The frequency of both the sources is 900 Hz. What is the value of

v_{1} - v_{2}

so that the beat frequency observed by the observer is 6 Hz? Speed of sound v = 300 m/s. Given that

v_{1}

and

v_{2}

≪ v.

1 m/s
2 m/s
3 m/s
4 m/s

Discuss Question

Answer: Option B. -> 2 m/s
:
B

f_{1} = 900 (\frac{300}{300 + v_{1}}) ≅ 900 {(1 + \frac{r_{1}}{300})}^{- 1} 900 - 3 v_{1}

Similarly,

f_{2} = 900 (\frac{300}{300 + v_{2}}) = 900 - 3 v_{2} f_{2} - f_{1} = 6 ∴ 3 (v_{1} - v_{2}) = 6 ∴ 3 (v_{1} - v_{2}) = 6 o r v_{1} - v_{2} = 2 m / s

Question 12. A train has just completed a U-curve in a track which is a semi-circle. The engine is at the forward end of the semi-circular part of the track while the last carriage is at the rear end of the semi-circular track. The driver blows a whistle of frequency 200 Hz. Velocity of sound is 340 m/s. Then the apparent frequency as observed by a passenger in the middle of the train, when the speed of the train is 30 m/s, is

219 Hz
188 Hz
200 Hz
181 Hz

Discuss Question

Answer: Option C. -> 200 Hz
:
C
The Doppler formula holds for non-collinear motion if v_s and v₀ are taken to be the resolved component along the line of slight, In this case, we have

A Train Has Just Completed A U-curve In A Track Which Is A S...

v_{0} = - v_{t} s i n 45^{\circ} = - \frac{30}{\sqrt{2}} m / s

v_{s} = - v_{t} s i n 45^{\circ} = \frac{30}{\sqrt{2}} m / s

We have, v = 340 m/s, n = 200 Hz. The apparent frequency n’ is given by

n^{'} = n [\frac{v - v_{0}}{v - v_{s}}] = 200 [\frac{340 + (\frac{30}{\sqrt{2}})}{340 + (\frac{30}{\sqrt{2}})}] = 200 H z

Question 13. Two factories are sounding their sirens at 800 Hz. A man goes from one factory to the other at a speed of 2 m/s. The velocity of sound is 320 m/s. The number of beats heard by the person in 1 s will be

Discuss Question

Answer: Option D. -> 10
:
D
When the man is approaching the factory,

n^{'} = (\frac{v + v_{0}}{v}) n = (\frac{320 + 2}{320}) 800 = (\frac{322}{320}) 800

When the man is going away from the factory,

n "= (\frac{v - v_{0}}{v}) n = (\frac{320 - 2}{320}) 800 = (\frac{318}{320}) 800 ∴ n^{'} - n "= (\frac{320 - 318}{320}) 800 = 10 H z

Question 14. A source of sound emits

200 π

W power which is uniformly distributed over a sphere of radius

10 m

. What is the loudness of sound on the surface of the sphere?

70 dB
107 dB
80 dB
117 dB

Discuss Question

Answer: Option D. -> 117 dB
:
D
Intensity,

I = \frac{P}{A} = \frac{200 π}{4 π \times (10)^{2}} = 0.5 W / m^{2}

Loudness =

10 l o g_{10} \frac{I}{I_{0}} = 10 l o g_{10} \frac{0.5}{10^{- 12}}

= 10 l o g_{10} (5 \times 10^{11})

= 10 l o g_{10} (\frac{10^{12}}{2})

= 117 dB

Question 15. A source of sound produces waves of wavelength 60 cm when it is stationary. If the speed of sound in air is 320 m/s and source moves with speed 20 m/s, the wavelength of sound in the forward direction will be approximately:

56.2 cm
60.8 cm
64.4 cm
68.6 cm

Discuss Question

Answer: Option A. -> 56.2 cm
:
A
Apparent frequency is given by:

n^{'} = n (\frac{v}{v - v_{s}})

For a medium, frequency is inversely proportional to wavelength.

λ^{'} = (\frac{v - v_{s}}{v}) λ

λ^{'} = (\frac{320 - 20}{320}) 60

λ^{'} = 56.25 c m

Question 16. One train is approaching an observer at rest and another train is receding from him with the same velocity 4 m/s. Both the trains blow whistles of same frequency of 243 Hz. The beat frequency in Hz as heard by the observer is (speed of sound in air is 320 m/s)

Discuss Question

Answer: Option B. -> 6
:
B
When the train is approaching,

n_{1} = \frac{v}{v - v_{s}} \times n = \frac{320}{320 - 4} \times 243 = \frac{80}{79} \times 243

When the train is receding,

n_{2} = \frac{v}{v + v_{s}} \times n = \frac{320}{324} \times 243 = \frac{80}{81} \times 243

Beat frequency is

n = n_{1} - n_{2} = 80 \times 243 (\frac{1}{79} - \frac{1}{81}) = 6 H z

Question 17. A man is watching two trains, one leaving and the other coming in with equal speed of 4 m/s. If they sound their whistles, each of frequency 240 Hz, the number of beats heard by the man (velocity of sound in air is 320 m/s) will be equal to

Discuss Question

Answer: Option A. -> 6
:
A
Apparent frequency due to train which is coming in is

m_{1} = \frac{v}{v - v_{s}} n

Apparent frequency due to train which is leaving is

m_{2} = \frac{v}{v - v_{s}} n

So the number of beats is

n_{1} - n_{2} = (\frac{1}{316} - \frac{1}{324}) 320 \times 240 \Rightarrow n_{1} - n_{2} = 6

Question 18. Two cars are moving on two perpendicular roads towards a crossing with uniform speeds of 72 km/h and 36 km/h. If second car blows horn of frequency 280 Hz, then the frequency of horn heard by the driver of first car when the line joining the cars makes angle of

45^{\circ}

with the roads, will be (velocity of sound is 330 m/s)

321 Hz
298 Hz
289 Hz
280 Hz

Discuss Question

Answer: Option B. -> 298 Hz
:
B
The component of velocity of source along line joining the car is

v_{s} = v_{1} c o s 45^{\circ} = 36 \times \frac{1}{\sqrt{2}} k m / h

= 5 \sqrt{2} m / s

Component of velocity of observer(second car) along the line joining the car is

Two Cars Are Moving On Two Perpendicular Roads Towards A Cro...

V_{0} = v_{2} c o s 45^{\circ} = 72 \times \frac{1}{\sqrt{2}} k m / h

= 10 \sqrt{2} m / s

n^{'} = \frac{v + v_{0}}{v - v_{s}} n = \frac{330 + 10 \sqrt{2}}{330 - 5 \sqrt{2}} \times 280

= \frac{344}{323} \times 280 H z = 298 H z

Question 19. A car emitting sound of frequency 500 Hz speeds towards a fixed wall at 4 m/s. An observer in the car hears both the source frequency as well as the frequency of sound reflected from the wall. If he hears 10 beats per second between the two sounds, the velocity of sound in air will be

330 m/s
387 m/s
404 m/s
340 m/s

Discuss Question

Answer: Option C. -> 404 m/s
:
C
The frequency that the observer receives directly from the source has frequency

n_{1} = 500 H z

. As the observer and source both move towards the fixed wall with velocity u, the apparent frequency of the reflected wave coming from the wall to the observer will have frequency

n_{2} = (\frac{V}{V - u}) 500 H z

where V is the velocity of sound wave in air. The apparent frequency of this reflected wave as heard by the observer will then be

n_{3} = (\frac{V + u}{V}) n_{2} = (\frac{V + u}{V}) (\frac{V}{V - u}) 500 = (\frac{V + u}{V - u}) 500

It is given, that the number of beat per second in

n_{3} - n_{1} = 10

∴ (n_{3} - n_{1}) = 10 = (\frac{V + u}{V - u}) 500 - 500 = 500 [\frac{V + u}{V - u} - 1] 10 = \frac{2 \times u \times 500}{V - u} H e n c e, 10 V = 1000 u + 10 u = 1010 u P u t t i n g u = 4 m / s, W e h a v e V = \frac{1}{10} [4040] = 404 m / s

Question 20. A whistle emitting a sound of frequency 440 Hz is tied to a string of 1.5 m length and rotated with an angular velocity of 20 rad/s in the horizontal plane. Then the range of frequencies heard by an observer stationed at a large distance from the whistle will be (v = 330 m/s)

400.0 Hz to 484.0 Hz
403.3 Hz to 480.0 Hz
400.0 Hz to 480.0 Hz
403.3 Hz to 484.0 Hz

Discuss Question

Answer: Option D. -> 403.3 Hz to 484.0 Hz
:
D
Frequency heard by the observes will be maximum when the source is in position D. In this case, source will be approaching towards the stationary observer, almost along the line of sight (as observer is stationed at a larger distance).

n_{m a x} = \frac{v}{v - v_{s}} n = \frac{330 \times 440}{330 - 1.5 \times 20} = 484 H z

A Whistle Emitting A Sound Of Frequency 440 Hz Is Tied To A ...

Similarly, frequency heard by the observer will be minimum when the source reaches at position B. now, the source will be moving away from the observer.