Problems

1. A source of sound of frequency 450 cycles/sec is moving towards a stationary observer with 34 m/sec speed. If the speed of sound is 340 m/sec, then the apparent frequency will be                   [MP PMT 1987]

A)            410 cycles/sec                      

B)            500 cycles/sec

C)            550 cycles/sec                      

D)            450 cycles/sec

Solution:

.

. The displacement of a particle is represented by the equation .This motion of particle is

A)           Simple harmonic with period

B)            Simple harmonic with period

C)            Periodic but not simple harmonic.

D)            Non- periodic

Solution:

As given that, y =

Velocity of the particle

So, acceleration,

In simple harmonic motion acceleration (or force) is directly proportional to the negative of displacement of particle as acceleration, a α –y

Hence, due to negative sign motion is simple harmonic motion (SHM.)

A simple harmonic motion is always periodic. So motion is periodic simple harmonic.

From the given equation,

Compare it by standard equation

So,

Hence, the motion is SHM with period.

3. The displacement of a particle is represented by the equation .This motion is

A)         Non- periodic 

B)          Periodic but not simple harmonic

C) Simple harmonic with period

D)          Simple harmonic with period

Solution:

A motion will be harmonic if a α displacement and a simple harmonic motion is always periodic but all simple harmonic motion are periodic but all periodic are not harmonic. As given equation of motion is

Again, differentiating both sides w.r.t ‘t’

So, is not directly proportional to y

So motion is not harmonic.

4. The relation between acceleration and displacement of four particles are given below

A)          

B)          

C)

D)           

Solution:

For motion to be SHM acceleration of the particle must be opposite of restoring force and proportional to negative of displacement. So,

i.e., ,

so Hence,

We should be clear that has to be linear.

5. The wavelength is 120 cm when the source is stationary. If the source is moving with relative velocity of 60 m/sec towards the observer, then the wavelength of the sound wave reaching to the observer will be (velocity of sound = 330 m/s)

(a) 98 cm 

(b) 140 cm

(c) 120 cm

(d) 144 cm

Solution:

=98cm

18. The frequency of a whistle of an engine is 600 cycles/sec is moving with the speed of 30 m/sec towards an observer. The apparent frequency will be (velocity of sound = 330 m/s)    [MP PMT 1989]

A)            600 cps        

B)            660 cps

C)            990 cps                                   

D)            330 cps

Solution:

19. An observer moves towards a stationary source of sound of frequency n. The apparent frequency heard by him is 2n. If the velocity of sound in air is 332 m/sec, then the velocity of the observer is  

A)            166 m/sec                              

B)            664 m/sec

C)            332 m/sec                              

D)            1328 m/sec

Solution:

.

20.  A whistle sends out 256 waves in a second. If the whistle approaches the observer with velocity 1/3 of the velocity of sound in air, the number of waves per second the observer will receive [MP PET 1990; DPMT 2002]

A)            384

B)            192

C)            300

D)            200

Solution:

Wave number = but = and

21. A person feels 2.5% difference of frequency of a motor-car horn. If the motor-car is moving to the person and the velocity of sound is 320 m/sec, then the velocity of car will be                     [CPMT 1981; MP PET 1989]

A)            8 m/s (approx.)                   

B)            800 m/s

C)            7 m/s                                       

D)            6 m/s (approx.)

Solution:

By Doppler’s formula =

Since, source is moving towards the listener so 

If n = 100 then n' = 102.5

22. Two passenger trains moving with a speed of 108 km/hour cross each other. One of them blows a whistle whose frequency is 750 Hz. If sound speed is 330 m/s, then passengers sitting in the other train, after trains cross each other will hear sound whose frequency will be        [MP PMT 1991]

A)            900 Hz                                     

B)            625 Hz

C)            750 Hz                                     

D)            800 Hz

Solution:

23. A source of sound is travelling towards a stationary observer. The frequency of sound heard by the observer is of three times the original frequency. The velocity of sound is v m/sec. The speed of source will be [MP PET 1991]

A)           

B)            v

C)           

D)            3v

Solution:

24. A sound source is moving towards a stationary observer with 1/10 of the speed of sound. The ratio of apparent to real frequency is [CPMT 1977; NCERT 1977; KCET 2001, 03]

A)            10/9                                         

B)            11/10

C)            (11/10)²

D)           (9/10)²

Solution:

25. The speed of sound in air at a given temperature is 350 m/s. An engine blows whistle at a frequency of 1200 cps. It is approaching the observer with velocity 50 m/s. The apparent  frequency in cps heard by the observer will be [CPMT 1976; RPET 1999; BHU 1997, 2001]

A)            600

B)            1050

C)            1400                                         

D)            2400

Solution:

= 1400 cps

26. Suppose that the speed of sound in air at a given temperature  is 400 m/sec. An engine blows a whistle at 1200 Hz frequency. It is approaching an observer at the speed of 100 m/sec. What is the apparent frequency as heard by the observer       [CPMT 1983; DPMT 2001]

A)            600 Hz                                     

B)            1200 Hz

C)            1500 Hz                                   

D)            1600 Hz

Solution:

27. A source of frequency 150 Hz is moving in the direction of a person with a velocity of 110 m/s. The frequency heard by the person will be (speed of sound in medium = 330 m/s)             [CPMT 1989; RPET 2001]

A)            225 Hz                                     

B)            200 Hz

C)            150 Hz                                     

D)            100 Hz

Solution:

28. A source of sound is moving with constant velocity of 20 m/s emitting a note of frequency 1000 Hz. The ratio of frequencies observed by a stationary observer while the source is approaching him and after it crosses him will be [MP PET 1994]

A)           9 : 8                                          

B)            8 : 9

C)            1 : 1                                          

D)            9 : 10

Solution:

When source is approaching the observer, the frequency heard 

When source is receding, the frequency heard

29. A source of sound S is moving with a velocity 50m/s towards a stationary observer. The observer measures the frequency of the source as 1000 Hz. What will be the apparent frequency of the source when it is moving away from the observer after crossing him ? The velocity of sound in the medium is 350 m/s              [MP PMT 1994]

A)            750 Hz                                     

B)            857 Hz

C)            1143 Hz                                   

D)            1333 Hz

Solution:

By using

30. A table is revolving on its axis at 5 revolutions per second. A sound source of frequency 1000 Hz is fixed on the table at 70 cm from the axis. The minimum frequency heard by a listener standing at a distance from the table will be (speed of sound = 352 m/s)      [MP PET 1996]

A)            1000 Hz                                   

B)            1066 Hz

C)            941 Hz                                     

D)            352 Hz

Solution:

For source S =0.70×2π×5 =22 m/sec

Minimum frequency is heard when the source is receding the man. It is given by

31. A source of sound S of frequency 500 Hz situated between a stationary observer O and a wall W, moves towards the wall with a speed of 2 m/s. If the velocity of sound is 332 m/s, then the number of beats per second heard by the observer is (approximately)

A)            8    

B)            6

C)            4    

D)            2

Solution:

For direct sound source is moving away from the observes so frequency heard in this case 

The other sound is echo, reaching the observer from the wall and can be regarded as coming from the image of source formed by reflection at the wall. This image is approaching the observer in the direction of sound.                   

Hence for reflected sound, frequency heard by the observer is 

32. A motor car blowing a horn of frequency 124vib/sec moves with a velocity 72 km/hr towards a tall wall. The frequency of the reflected sound heard by the driver will be (velocity of sound in air is 330 m/s)                      [MP PET 1997]

A)            109 vib/sec                            

B)            132 vib/sec

C)            140 vib/sec                            

D)            248 vib/sec

Solution:

= 140 vib/sec