Waves and Vibrations

Physics · 11th Class (Intermediate Part 1) · BISE Lahore

70 questions

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20 questions · Measurements × 1, Force and Motion × 2, Circular and Rotational Motion × 2, Work, Energy and Power × 1, Solids and Fluid Dynamics × 2, Heat and Thermodynamics × 1, Waves and Vibrations × 3, Physical Optics and Gravitational Waves × 1, Electrostatics and Current Electricity × 3, Electromagnetism × 2, Special Theory of Relativity × 1, Nuclear and Particle Physics × 1

Waves and Vibrations Test

10 questions · Waves and Vibrations × 10

Sample questions

Showing 20 of 70 questions from this chapter. The full bank is in the chapter test below.

1
The speed $v$ of a wave of frequency $f$ and wavelength $\lambda$ is given by
- A. $v = f\lambda$ (correct answer)
- B. $v = f/\lambda$
- C. $v = \lambda/f$
- D. $v = f + \lambda$
Why: One crest advances by exactly one wavelength in one period, so $v = \lambda/T$ , and since $1/T = f$ this gives $v = f\lambda$ . The other choices invert the relation or add quantities that have different units.
2
The wavelength of a wave is the distance between
- A.the equilibrium position and the next crest
- B.two consecutive points on the wave that are in phase (correct answer)
- C.a crest and the next trough
- D.two consecutive nodes of the wave pattern
Why: Points that are in phase have the same displacement and the same direction of motion, and the shortest distance between such points is one wavelength. The crest to trough distance and the distance between neighbouring nodes are each only half a wavelength.
3
The amplitude of a wave is
- A.the distance travelled by the wave in one second
- B.the number of complete oscillations made in one second
- C.the maximum displacement of the particles from their equilibrium position (correct answer)
- D.the time taken for one complete oscillation
Why: Amplitude is the largest displacement of a particle of the medium from its rest position, and it fixes how much energy the wave carries. The number of oscillations per second is the frequency, not the amplitude.
4
The frequency of a wave is the number of
- A.wavelengths contained in one metre of the wave
- B.seconds taken to complete one oscillation
- C.metres covered by the wave in one second
- D.oscillations or cycles completed in one second (correct answer)
Why: Frequency counts complete vibrations per second and is measured in hertz. Seconds per oscillation is the time period, which is the reciprocal of the frequency.
5
A source vibrates with a frequency of $50\ \mathrm{Hz}$ . The time period of the wave produced is
- A. $0.02\ \mathrm{s}$ (correct answer)
- B. $0.2\ \mathrm{s}$
- C. $2\ \mathrm{s}$
- D. $50\ \mathrm{s}$
Why: The period is the reciprocal of the frequency, $T = 1/f = 1/50\ \mathrm{s} = 0.02\ \mathrm{s}$ . The value 0.2 s is a factor of ten too large, a common slip when dividing by 5 instead of 50.
6
A sound wave of frequency $500\ \mathrm{Hz}$ travels through air with a speed of $340\ \mathrm{m\,s^{-1}}$ . Its wavelength is
- A. $1.47\ \mathrm{m}$
- B. $0.68\ \mathrm{m}$ (correct answer)
- C. $0.34\ \mathrm{m}$
- D. $170000\ \mathrm{m}$
Why: $\lambda = v/f = 340/500\ \mathrm{m} = 0.68\ \mathrm{m}$ . Dividing the frequency by the speed instead gives 1.47 m, which is the reciprocal of the correct value.
7
Which one of the following waves can travel through vacuum?
- A.A sound wave
- B.A wave on a stretched string
- C.An electromagnetic wave (correct answer)
- D.A seismic wave
Why: Electromagnetic waves need no material medium, which is how energy reaches the Earth from the Sun across empty space. Sound, string waves and seismic waves are mechanical and die out without a medium.
8
Sound cannot travel through vacuum because
- A.its frequency becomes zero in vacuum
- B.its wavelength becomes infinite in vacuum
- C.vacuum absorbs all the sound energy
- D.there are no particles in vacuum to carry the vibration (correct answer)
Why: Sound is a mechanical wave and is propagated by the to and fro motion of the particles of the medium, so with no particles there is nothing to pass the disturbance on.
9
In a transverse wave, the particles of the medium vibrate
- A.at right angles to the direction in which the wave carries energy (correct answer)
- B.along the direction in which the wave carries energy
- C.in a circular path about the source
- D.along the direction of energy travel but with a smaller speed
Why: A transverse wave has its vibrations perpendicular to the direction of energy travel, as in a wave on a plucked string. Vibrations parallel to the direction of travel belong to a longitudinal wave.
10
In a longitudinal wave, the regions in which the particles of the medium are closest together are called
- A.crests
- B.compressions (correct answer)
- C.troughs
- D.antinodes
Why: A longitudinal wave consists of compressions, where the particles crowd together, and rarefactions, where they spread apart; these play the same role as the crests and troughs of a transverse wave.
11
The principle of superposition of waves states that the resultant displacement of a particle acted on by two waves at the same instant is
- A.the product of the two individual displacements
- B.always equal to the larger of the two displacements
- C.the algebraic sum of the two individual displacements (correct answer)
- D.always equal to zero
Why: The individual displacements are added together, taking their signs into account, to give the resultant displacement. The other choices would either change the dimensions of the result or ignore the contribution of one wave.
12
Two identical waves of amplitude $y_0$ arrive at a point in phase with each other. The amplitude of the resultant disturbance there is
- A.zero
- B. $y_0$
- C. $4y_0$
- D. $2y_0$ (correct answer)
Why: In-phase displacements add, so $y = y_0 + y_0 = 2y_0$ . A resultant of zero would need the two waves to be exactly out of phase.
13
Two identical waves meet at a point half a cycle out of step with each other. The resultant displacement at that point is
- A.zero (correct answer)
- B. $y_0$
- C. $2y_0$
- D. $4y_0$
Why: The two displacements are equal and opposite, so their algebraic sum is $y_0 - y_0 = 0$ and the particle shows no displacement at all.
14
The principle of superposition applies to
- A.waves of very large amplitude only
- B.linear waves of small amplitude (correct answer)
- C.shock waves that permanently change the medium
- D.sound waves only, whatever their amplitude
Why: For small amplitude linear waves the response of the medium stays proportional to the disturbance, so displacements may simply be added. Very large amplitude waves distort the medium and no longer obey this simple addition.
15
Interference of waves is produced by the superposition of two waves that have the same frequency and travel
- A.in opposite directions through the same medium
- B.at right angles to each other
- C.in the same direction through the same medium (correct answer)
- D.with amplitudes that differ by a factor of two
Why: Two waves of equal frequency travelling in the same direction give the steady pattern of reinforcement and cancellation called interference. Equal frequency waves travelling in opposite directions give a stationary wave instead.
16
Two sources of waves are said to be coherent when they emit waves of
- A.the same amplitude but different frequencies
- B.different frequencies with a constant phase difference
- C.the same amplitude with a rapidly changing phase difference
- D.the same frequency with a constant phase difference (correct answer)
Why: Coherent sources have a fixed phase relationship, which is why the interference pattern keeps the same shape and can be observed steadily. If the phase difference changes rapidly the bright and dark regions shift and no steady pattern is seen.
17
Constructive interference occurs at points where the path difference between the two waves is
- A. $n\lambda$ , where $n = 0, 1, 2, 3, ...$ (correct answer)
- B. $(2n+1)\frac{\lambda}{2}$
- C. $\frac{\lambda}{4}$
- D. $(2n+1)\lambda$
Why: When the path difference is a whole number of wavelengths the two waves arrive in phase and their displacements add, giving a large resultant. The half wavelength conditions in the other options give cancellation instead.
18
Two waves reach a point with a path difference of $(2n+1)\frac{\lambda}{2}$ , where $n = 0, 1, 2, 3, ...$ . The resultant displacement at that point is
- A.equal to the larger of the two amplitudes
- B.zero (correct answer)
- C.equal to half the sum of the two amplitudes
- D.equal to the sum of the two amplitudes
Why: An odd multiple of half a wavelength puts the two waves exactly out of phase, so a crest of one meets a trough of the other and their displacements cancel. A path difference of a whole number of wavelengths would instead give the sum of the amplitudes.
19
Two loudspeakers emit sound waves of wavelength $0.5\ \mathrm{m}$ . At a point where the path difference between the two waves is $1.5\ \mathrm{m}$ , the interference is
- A.destructive, because the path difference is an odd multiple of half the wavelength
- B.destructive, because the path difference is an odd multiple of the wavelength
- C.constructive, because the path difference is an integral multiple of the wavelength (correct answer)
- D.neither constructive nor destructive, because the path difference is not a whole number of wavelengths
Why: Here $1.5\ \mathrm{m} = 3\lambda$ , an integral multiple of the wavelength, so the waves arrive in phase and reinforce each other to give a loud sound.
20
Two loudspeakers $3.0\ \mathrm{m}$ apart emit a note of frequency $344\ \mathrm{Hz}$ . Along a line $4.0\ \mathrm{m}$ in front of them, a microphone lies $5.0\ \mathrm{m}$ from one speaker and $4.0\ \mathrm{m}$ from the other, where the sound is loudest. The speed of sound is
- A. $172\ \mathrm{m\,s^{-1}}$
- B. $300\ \mathrm{m\,s^{-1}}$
- C. $688\ \mathrm{m\,s^{-1}}$
- D. $344\ \mathrm{m\,s^{-1}}$ (correct answer)
Why: The path difference is $5.0 - 4.0 = 1.0\ \mathrm{m}$ , and the first loud point away from the centre means this path difference equals one wavelength, so $v = f\lambda = 344 \times 1.0\ \mathrm{m\,s^{-1}} = 344\ \mathrm{m\,s^{-1}}$ .

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