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Q1. Two tuning forks are struck and the sounds from each reach your ears at the same time. One sound has a frequency of 256 Hz, and the second sound has a frequency of 258 Hz. The underlying beat frequency is:

• 2.0 Hz
• 256 Hz
• 258 Hz
• 257 Hz

Solution

The beat frequency is the difference between the two frequencies; f(beat) = 258 Hz - 256 Hz = 2 Hz.

Q2. A spectral line of wave length 5000 A.U in the light coming from a distant star is observed to be shifted to 5004 A.U.  The component of the recessional velocity of the star along the line of sight is :

• 1.4 x 10⁵ m/s
• 1.8 x 10⁵ m/s
• 2.0 x 10⁵ m/s
• 2.4 x 10⁵ m/s

Solution

We have v =zc where z = ( Therefore, the recessional velocity = Note that you can substitute the wave length in the given unit itself since z is a ratio of wave lengths.

Q3. Properties of a kind of wave are given below. Identify the type of wave i. Wave can not be detected by human ear ii. Velocity of wave in free space is 3x10⁸m/s iii. Velocity is not effected by temperature iv. Waves can travel through vacuum

• Radio waves
• Water waves
• Tidal waves
• Sound waves

Solution

The properties mentioned are of transverse waves. Among the options given the Radio waves are the only transverse waves.

Q4. A sound source of frequency 600 Hz is moving towards an observer with velocity 20 m/s. The speed of sound is 340m/s. The frequency heard by observer will be

• 30 Hz
• 630.5 Hz
• 637.5 Hz
• 63.5 Hz

Solution

Q5. On adding two sine waves that are exactly the same, what would be the result?

• an identical sine wave
• an identical sine wave with half the amplitude
• an identical sine wave with double the amplitude
• an identical sine wave with double the frequency

Solution

On adding two sine waves that are exactly the same, we get an identical sine wave with double the amplitude in accordance with the superposition principle..

Q6. Standing waves result from the superposition of two waves that have:

• the same amplitude, frequency, and direction of propagation
• the same amplitude and frequency and opposite directions of propagation
• the same amplitude, slightly different frequencies, and the same direction of propagation
• the same amplitude, slightly different frequencies, and opposite directions of propagation

Solution

Standing waves are the consequence of the constructive interference of waves that have the same amplitude and frequency but are traveling in opposite directions.

Q7. Wavelength of a progressive wave is the distance between two

• consecutive points of the same phase at a given time.
• alternate points of the same phase at a given time
• consecutive points out of phase by 180 degrees
• consecutive points out of phase by 90 degrees

Solution

Wavelength of a progressive wave is the distance between two consecutive points of the same phase at a given time.

Q8. In a wave, which quantity is transferred from one point to the other?

• matter
• energy
• wavelength
• frequency

Solution

In a wave, the energy is transferred from one point to the other.

Q9. As a wave propagates; which of the following is not satisfied?

• the wave intensity remains constant for a plane wave
• the wave intensity decreases as the inverse of the distance from the source for a spherical wave
• the wave intensity decreases as the inverse of the square of the distance from the source for a spherical wave
• total intensity of the spherical wave over the spherical surface centered at the source remains constant at all times

Solution

As a wave propagates, the wave intensity decreases as the inverse of the square of the distance from the source for a spherical wave.

Q10. Maximum destructive inference between two waves occurs when the waves are out of the phase by

• π radians
• π/4 radians
• π/2radians
• π/3 radians

Solution

Destructive inference between two waves occurs when the waves are out of the phase by π radians.

Q11. A travelling wave in a stretched string is described by the equation; y = a sin ( Kx - ωt). The maximum particle velocity is:

• Aω  
•   ω / k  
• Dω/dk
• x/ω

Solution

Velocity = dy/dt Max. velocity = A ω

Q12. A radio station broadcasts programs at wave frequency 20 Megacycles/sec. What would be their wavelength?

• 5 m
• 15 m
• 10 m
• 20 m

Solution

Q13. In Doppler effect change in frequency depends on

• speeds of source and listener  
• distance between source and listener
• density of air
• half of distance between source and listener

Solution

Speeds of source and listener helps in analyzing the shift in frequency in Doppler effect.

Q14. The apparent frequency of the whistle of an engine changes in the ratio 9:8 as the engine passes a stationary observer. If the velocity of the sound is 340 ms^-1, then the velocity of the engine is:

• 40 m/s
• 20 m/s
• 340 m/s
• 180 m/s

Solution

When the engine approaches the observer, the apparent frequency is v/(v-v_S) and when it moves away from the observer, the apparent frequency is v/(v+v_S).  The frequency therefore changes in the ratio (v+v_S)/(v-v_S).  We have therefore, (v+v_S) / (v-v_S) = 9/8 from which the velocity of the source, v_S = v/17 = 340/17 = 20m/s.

Q15. Doppler effects would not hold for

• Electromagnetic waves
• Micro waves
• Radio waves
• Circular waves

Solution

Doppler effects would not hold for circular waves

Q16. If the source of sound moves at the same speed or faster than speed of the wave then it results in

• Doppler effect
• Beats
• Shock waves
• Refraction of sound

Solution

If the source of sound moves at the same speed or faster than speed of the wave then it results in shock waves.

Q17. The frequency of tuning forks A and B are respectively 3% more and 2% less than the frequency of tuning fork C. When A and B are simultaneously excited, 5 beats per second are produced. Then the frequency of the tuning fork 'A' (in Hz) is

• 98
• 100
• 103
• 105

Solution

Q18. If you are standing next to the road, why does the pitch of the siren of police car change as it comes toward you?

• Relative velocity changes as its angle with respect to you changes as the police car approaches you .
• Speed of sound increases
• The pitch is constant until the ambulance passes by
• The pitch seems to changes, due to changing in air pressure

Solution

Relative velocity changes as its angle with respect to you changes as the police car approaches you .

Q19. Waves associated with moving protons, electrons, neutrons, atoms are known as

• Electromagnetic waves
• Gamma rays
• Matter waves
• Matter waves

Solution

Waves associated with moving protons, electrons, neutrons, atoms are known as matter waves.

Q20. The number of beats produced per second by the vibrations x₁ = A sin (420 πt) and x₂ = A sin (424 πt) is

• 4
• 6
• 1
• 2

Solution

Q21. Doppler effect would take place in case of

• Source and listener both move in same direction with the same speed
• When both source and listener both are at rest and wind is blowing
• When one of the source or listener is at the centre of a circle, while the other is moving on it with uniform speed
• Detecting new planets with help of Doppler shift of light

Solution

Doppler effect would take place while detecting new planets with help of Doppler shift of light.

Q22. A radar sends a radio signal of frequency 9 x 10⁹ Hz towards an aircraft approaching the radar.  If the reflected wave shows a frequency shift of 3 X 10³ Hz, the speed with which the aircraft is approaching the radar in m/s is (velocity of radio signal is 3 X 10⁸ m/s).

• 150
• 100
• 50
• 25

Solution

The source of waves in this problem is the reflected image of the radar, the aircraft functioning as a mirror.  The velocity of the reflected image is twice the velocity of the 'mirror' (aircraft).  You have to note this while calculating the velocity (v_S) of the source using the equation involving 'blue shift' discussed in the beginning of this post : v_S = c(n^'-n)/n^' = 3 X 10⁸ (3 x 10³)/(9 x 10⁹) = 100 m/s. The velocity of aircraft is half that of the reflected image (source).  So the answer is 50 m/s.

Q23. What would be the fundamental frequency of a 20 cm long close ended pipe? Would it resonantly be excited by a 430 Hz source?(Take speed of sound as 340 m/s)

• 425 Hz, yes
• 415 Hz, yes
• 400 Hz, no
• 430 Hz, yes

Solution

 

Q24. If a source of sound was moving toward a receiver at 1/3 the speed of sound, what would the resulting wavelength be?

• 1/3 of the emitted wavelength
• Can not be found
• 2/3 of the emitted wavelength
• 6  times the emitted wavelength

Solution

Q25. The speed of transverse waves in a string depends on:

• Tension in it and its linear mass density
• Young's modulus and linear mass density
• Shear modulus and linear mass density
• Pressure on the string

Solution

where T is the tension in it and μ is its linear mass density.  

Q26. A wave travelling along a string is described by y (x,t)=0.005 sin(95.0x-4.0t) what would be its angular wave number, k and wavelength, λ?

• 6.01m
• 6.66 cm
• 6.61cm
• 6.61m

Solution

Q27. Doppler's effect in sound is:

• Symmetrical
• Superimposing
• Asymmetrical
• Infinite

Solution

Doppler's effect in sound is asymmetrical.

Q28. A person moves away with constant velocity 'v₀' from a stationary train which blows its whistle.  The ratio of the real frequency of the whistle to the apparent frequency as measured by the person is 1.25.  If the person is stationary and the whistle is moving away from the person with the same velocity 'v₀', the ratio of the real frequency of the whistle to the apparent frequency as measured by the person will be

• 1.2
• 1.25
• 1.4
• 1.45

Solution

The apparent frequency (n₁) as measured by the person moving away from the whistle with velocity v_L is given by n₁ = n(v-v_L)/v where 'n' is the real frequency of the whistle and 'v' is the velocity of sound. Therefore, n/n₁ = v/(v-v_L) = v/(v-v₀). Since n/n₁ = 1.25, we have v/(v-v₀) = 1.25 so that 1 - (v₀/v) = 0.8 from which v₀ = 0.2v. If the person is stationary and the whistle is moving away from the person with the same velocity 'v₀', the apparent frequency (n₂) as measured by the person is given by n₂ = nv/(v+v_S) where v_S=v₀ Therefore, n/n₂ = (v+v₀)/v Substituting for v₀ (=0.2v) we obtain n/n₂ = (v+0.2v)/v = 1.2

Q29. A node is a point where there is always

• Double trough
• Destructive interference
• Constructive interference
• Two crests

Solution

A node is a point where there is always destructive interference.  

Q30. Waves produced in a cylinder containing a liquid by moving its piston back and forth. The wave motion in this case is:

• transverse
• longitudinal
• combination of both transverse and longitudinal
• None of the above

Solution

The wave motion in this case is a combination of transverse and longitudinal.

Q31. The notes of frequency equal to or an integral multiple of fundamental frequency are called

• Beats
• Overtones
• Harmonics
• Pitch

Solution

The notes of frequency equal to or an integral multiple of fundamental frequency are called beats.

Q32. Which of the following waves can be polarized?

• Light waves
• Sound waves
• Electro magnetic waves
• Water waves

Solution

Polarization is the property shown by transverse waves.

Q33. Speed of the sound in a perfectly rigid rod would be

• Dubbed
• Damp
• Oscillating
• Infinite

Solution

Speed of the sound in a perfectly rigid rod would be infinite.

Q34.  A train is moving on a straight track with speed 20 ms^-1. It is blowing its whistle at  the frequency of 1000 Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound = 320 ms^-1) close to:

• 6 %
• 12 %
• 18 %
• 24%

Solution

A train is moving on a straight track with speed v_s = 20 m/s. It is blowing its whistle at the frequency of f₀ = 1000 Hz.The frequency of the whistle heard by the person standing near the track is given as: As the train approaches the person: As the train goes away from the person: The percentage change in the frequency heard by the person standing near the track as the train passes him is given as: Thus, the frequency heard by a person standing near the track changes by 12 % as the train passes him.

Q35. A standing wave is formed when ____.

• a wave reflects due to changes in the properties of the medium.
• a wave reflects off a  wall
• air is compressed in a cylinder
• two identical waves moving in opposite directions along the same medium interfere

Solution

A standing wave is formed when two identical waves moving in opposite directions along the same medium interfere with each other.

Q36. A police car moving at 22 m/s, chases a motor cyclist.  The police man sounds his horn at 176 Hz while both of them move towards a stationary siren of frequency 165 Hz.  Calculate the speed of the motor cyclist, if it is given that he does not hear any beats. (Velocity of sound = 330 m/s).

• 33 m/s
• 22 m/s
• zero
• 11 m/s

Solution

Since the motor cyclist does not hear any beats, the apparent frequency of the horn of the police car (as heard by the motor cyclist) is the same as the apparent frequency of the stationary siren.  Therefore, we have, n(v-v_L)/(v-v_S) = n^'(v+v_L)/v where v is the velocity of sound, v_L is the velocity of the motor cyclist, v_S is the velocity of the police car and n and n^' are the frequencies of the police car horn and the stationary siren respectively.  Substituting for the velocities, we obtain 176(330-v_L)/(330-22) = 165(330+v_L)/330, from which v_L = 22 m/s.

Q37. What would be the change in the speed of wave if tension in wire is increased nine times?

• remains same
• Becomes thrice
• Decrease to half its original speed
• Increases continuously

Solution

Speed of wave is directly proportional to √T so speed becomes thrice if tension is increased nine times.

Q38. Which instrument works on the basis of reflection of sound waves?

• Microscope
• Telescope
• Stethoscope
• Horoscope

Solution

A stethoscope works on the basis of reflection of sound waves, wherein the sound waves from different organs travel get reflected inside the tube and travel to the ears.

Q39. Pure sound notes from two sources make the molecules of air at a location vibrate simple harmonically in accordance with the equations. y₁ = 0.008 sin (604 π t) and y₂ = 0.007 sin (610 π t) respectively. The number of beats heard by a person at the location will be:  

• 1
• 2
• 3
• 4

Solution

The expression are of the simplest form of simple harmonic motion, y = a sin ωt where y is the displacement at the instant t, a is the amplitude, and ω is the angular frequency. The angular frequency ω is related to the linear frequency f as ω = 2πf. The linear frequencies of the two sound are therefor 302 Hz and 305 Hz. [2πf₁ = 604 π and 2πf₂ = 610π] The number of beats heard is 305 - 302 = 3  

Q40. Fundamental note in open pipe (v₁= ν/2L) has _________ the frequency of the fundamental note in closed organ pipe (v₂=ν/4L).

• Twice
• Half
• Thrice
• Four times