11 Wave Motion

Question 1

Explain the term progressive wave.
Explain whether the particles in the medium move with the wave.

Answer 1

A progressive wave transports energy from one point to another in the direction of wave propagation. The particles in the medium do not move with the wave as they merely oscillate about their equilibrium positions/undisturbed positions.

Question 2

Define displacement of a wave.

Answer 2

The displacement of a particle on a wave is the distance it travelled in a specific direction from its equilibrium position.

Question 3

Define the amplitude of a wave.

Answer 3

The amplitude of a wave is the magnitude of the maximum displacement of a particle in a wave from its equilibrium position.

Question 4

Define the period of a wave.

Answer 4

The period of a wave is the time taken for a particle to complete one oscillation.

Question 5

Define the frequency of a wave.

Answer 5

The frequency of a wave is the number of oscillations per unit time made by a particle of a wave. Note: It does not have to be complete oscillations as frequency does not have to be a whole number.

Question 6

Define the wavelength of a wave.

Answer 6

The wavelength of a wave is the distance between two consecutive points which are in phase.

Question 7

Define the speed of a wave.

Answer 7

The speed of a wave is the distance travelled by the wave over time taken.

Question 8

Define phase or phase angle.
Explain how particles may be in phase or out of phase.
Explain the term phase difference.

Answer 8

The phase of a wave is an angle that gives a measure of the fraction of a cycle that has been completed by an oscillating particle or by a wave.

Particles are considered to be in phase when they execute the same motion at the same time. (Pass through the equilibrium position at the same time in the same direction/in the same stage of oscillation/same displacement, velocity and acceleration)

Particles are considered to be out of phase when they show different stages of motion and hence have a non-zero phase difference

The phase difference between two particles in a wave is a fraction of a complete oscillation by which one is ahead of the other. It is usually expressed as an angle in radians.

Question 9

Explain the term wavefront. In which direction does wave travel in relation to its wavefront?

Answer 9

Wavefront is a line or surface joining points on a wave that are in phase. The wave travels in a direction that is perpendicular to the wavefront.

Question 10

Deduce the formula for the speed of a wave.

Answer 10

In a time of one period, the waveform moves a distance of one wavelength. Hence, v = distance/time = wavelength/period. Since frequency = 1/period, v = frequency of wave*wavelength of wave.

Question 11

Define the intensity of a wave. State the origin of a energy of a wave and the equation to calculate the total energy of an oscillating particle.

Answer 11

The intensity of a wave is defined as the rate of transfer of energy per unit area normal to the direction of the propagation of the wave (where I =P/S and P is the power of the source, S is the surface area).

The energy of a wave comes from the oscillations of its fields (electromagnetic radiation)/from the oscillations of the particles in the medium (mechanical waves).

The total energy of an oscillating particle = 1/2 * mw^2X0^2 where w refers to the angular frequency of the particle

Question 12

State the equation that relates intensity I to amplitude A.

Answer 12

I is proportional to A^2

Question 13

Consider a point source emitting waves that spread out radially in all directions. State the law that governs the intensity of a point source of a wave.

Answer 13

Energy will spread over an expanding spherical wavefront. The further away from the source, the larger the area the energy is distributed. Hence, the intensity of the wave decreases.

I = P/4pir^2 where P is the power of the source and r is its distance from the source.

If the power of the source is constant, intensity is inversely proportional to the square of the distance from the source r: I = k/r^2. This is known as the inverse square law.

Question 14

When does the intensity of a wave remain unchanged as it progresses?

Answer 14

For an ideal plane-wave source, the intensity of the plane waves remains constant.

Question 15

Define transverse wave. Give examples of transverse waves.

Answer 15

A transverse wave is one in which its particles oscillate in a direction perpendicular to the direction of energy transfer. E.g. EM waves, pulses in ropes

Question 16

Define longitudinal wave. Gives examples of longitudinal waves.

Answer 16

A longitudinal wave is one in which its particles oscillate in a direction parallel to the direction of energy transfer. E.g. sound waves, longitudinal pulses in springs

Question 17

State the important properties of EM waves.

Answer 17

EM waves do not require a medium to propagate; they can travel through a vacuum.

EM waves travel at the speed of c = 3.00*10^8 ms^-1 in a vacuum

EM waves are transverse waves and hence can be polarised.

Question 18

State the electromagnetic spectrum

Answer 18

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Question 19

Describe sound waves. How do you find the wave length of a sound wave?

Answer 19

Sound waves are longitudinal waves.

The regions where the air particles are compressed together and other regions where the air particles are spread far apart are known as compressions C and rarefactions R respectively. C are regions of high air pressure where the pressure variation against the displacement graph is above the x-axis as the pressure variation is compared to atmospheric pressure. R are regions of low air pressure where the pressure variation against the displacement graph is below the x-axis. In between C and R is a point where the pressure is equal to the atmospheric pressure. Since a sound wave consists of a repeating pattern of high-pressure and low-pressure regions moving through a medium, it is sometimes referred to as a pressure wave.

In a longitudinal wave, a wavelength is a distance between 2 consecutive Cs or Rs.

Question 20

Define polarisation.

Answer 20

Polarisation is a phenomenon whereby the oscillations of the wave particles in transverse waves are restricted to one direction only and this direction is perpendicular to the direction of energy transfer

Question 21

Describe the direction in which electric fields oscillate for unpolarised light.

Answer 21

Light is a transverse electromagnetic wave and is generally unpolarised, all planes of polarisation being present. For unpolarised light, the electric field can oscillate in any direction perpendicular to the direction of energy transfer.

Question 22

Describe what happens when an unpolarised EM wave passes through a linear polariser.

Answer 22

A plane-polarised wave is produced and the wave is said to be linearly polarised in the plane parallel to the polarising axis of the filter (in the vertical direction, along the polarising axis).

Question 23

Define an ideal polariser. Describe the changes to the intensity of unpolarised light when it is incident on an ideal polariser. State whether it is possible to compare the amplitudes between unpolarised and polarised waves.

Answer 23

An ideal polariser is a material that only allows the electric field vector of an EM wave that is paralllel to the polarizing axis to pass through and not the electric field perpendicular to the polarising axis.

Since the incident light is a random mixture of all polarisation states, the components of the electric field vectors that are perpendicular or parallel to the polarising axis are equal. Hence, by only transmitting the component that is parallel to the polarising axis, only half the incident intensity is transmitted. However, it is not possible to compare the amplitudes between unpolarised and polarised waves.

Hence, Initial intensity = 2*final intensity

Question 24

State Malus’ Law.

Answer 24

Malus’ Law states that the intensity of a beam of plane-polarised light after passing through a polariser varies with the square of the cosine of the angle through which the polariser is rotated from the position that gives maximum intensity.

The intensity of an EM wave is proportional to the square of the amplitude of the wave, implying that the intensity of the transmitted wave can be expressed as I = I0cos^2theta where I0 is the intensity of the light before passing through the analyser.