Longitudinal & Transverse Waves (AQA A Level Physics)

State what is meant by polarisation and explain how it is used to distinguish between transverse and longitudinal waves.

An unpolarised light source passes horizontally through a fixed polarising filter A. An observer views the light emerging through a second polarising filter B, which may be rotated about point XY as shown in Figure 1.

Figure 1

The observer rotates B slowly through 360° clockwise. 

Relative to polarising filter A, at which angles of polarising filter B does the observer see the maxima and minima amount of daylight.

On Figure 2 below, sketch how the light intensity reaching the observer varies as polarising filter B is rotated slowly through 360°.

Figure 2

Explain why when the transmission axis of polarising filter B is perpendicular to the plane XY, the observer does not see horizontally polarised light. 

Figure 1 represents a progressive wave travelling from left to right on a stretched string.

Figure 1

The frequency of the wave is 30 Hz. Calculate the speed of the wave.

State the phase difference between points X and Y on the string, giving an appropriate unit.

Describe how the vertical displacement of point X on the string varies in the next period.

Determine the phase difference between the current position of X and the position of X 0.0825 s later.

Explain briefly how transmission of energy by a longitudinal wave differs from transmission of energy by a transverse wave. Give one example of a transverse wave.

With the aid of a clearly labelled diagram explain how a sound wave in air transmits energy away from its source.

Short pulses of sound are reflected from a wall 30 m from the sound source. The reflected pulses return to the source after 0.18 s.

Calculate the speed of sound.

Figure 1 represents the sound wave from part (c).

Figure 1

Calculate the frequency of the sound wave.

Figure 1 shows two ways in which a wave can travel along a slinky spring.

Figure 1

Use arrows to draw the direction in which the points Q and R are about to move as each wave moves to the right.

State which wave in part (a) electromagnetic waves are similar in nature to. 

Hence or otherwise, explain why it is important to correctly align a radio antenna in order to receive the strongest signal.             

Light from a filament lamp is viewed through two polarising filters A and B shown in Figure 2.

Figure 2

Explain why the observer cannot see the light from the filament lamp.

Explain how polaroid sunglasses can be used to view objects under the surface of water on a sunny day.

Explain the difference between compressions and rarefactions in a longitudinal wave.

Musicians can use tuning forks to tune their instruments.

A tuning fork produces a specific frequency when it vibrates. 

Figure 1 shows a tuning fork vibrating in air at a single instant in time. The circles represent the positions of air particles in the sound wave.

Figure 1

The tuning fork is used to tune an orchestra at 0.44 kHz. 

Air particles vibrate in different phases in the direction in which the wave is travelling. 

Calculate the minimum separation of particles that vibrate 90° out of phase. 

            Speed of sound in air = 340 m s^–1.     

Figure 2 shows a snapshot of a progressive wave travelling from left to right on a violin string stretched between points X and Y. The violin is tuned to the same frequency as the tuning fork.

Figure 2

State the phase relationship between points A and B on the string. Label two more points, P and Q on Figure 2 which are  radians out of phase.

Points X and Y in Figure 2 are 0.84 m apart. 

Calculate the speed of the wave travelling along the string.

Figure 1 shows a vertical cross-section through a water wave moving from left to right.

Figure 1

Deduce the point at which the water is moving at maximum speed and explain your reasoning. 

While a microphone is connected to an oscilloscope, a student strikes a tuning fork nearby. 

The sound wave produced by the tuning fork is displayed as a trace on the screen. Figure 2 shows the resulting trace.

Figure 2

Use Figure 2 to calculate the wavelength of the sound wave produced. 

(The speed of sound is approximately 330 m s^–1).

The student’s lab partner strikes another identical tuning fork near the microphone, so that both sound wave signals can be overlaid on the oscilloscope trace. Figure 3 shows the new trace.

Figure 3

Using Figure 3, determine the phase difference between the two signals as shown on the oscilloscope trace. 

Give a suitable unit with your answer.

The oscilloscope trace is known as a ‘time-view’ of the sound wave because it shows the displacement of an oscillating signal against time. One of the students makes a time-view sketch as shown in Figure 4a, including a label M. 

An oscillating signal can also be shown in terms of a ‘space-view’, which would show the displacement of the signal against its position. The other student makes a space-view sketch as shown in Figure 4b, including a label N.

Figure 4a

Figure 4b

Show that the wave speed v is given by:

                  V=

Transverse progressive sinusoidal waves of wavelength λ travel along a horizontal rope. 

P and Q are points on the rope  apart and the waves travel from P to Q. 

With an appropriate sketch, discuss the motion of Q at the instant when P is displaced upwards but is moving downwards.

Electromagnetic waves carry energy through the vacuum of space as progressive transverse waves. 

Discuss the motion of an electromagnetic wave with reference to the appropriate fields.

Einstein famously discovered an equation called the ‘energy relation’, which gives the energy E of any particle in terms of its momentum p and mass m: 

                  E² = (pc)² + (mc²)² 

One of the surprising consequences from this equation is that electromagnetic waves also carry momentum p through the vacuum of space. 

Using knowledge of photons in the electromagnetic spectrum and Einstein’s energy relation, show that the photon momentum p is given by the equation: 

                  p =

Electromagnetic waves, being transverse, can also be polarised.

A light source is viewed through two pieces of polarisers, A and B, with their axes initially at  radians from each other, as shown in Figure 1.

Figure 1

Using the axes below, sketch the variation of intensity of light reaching the eye with angular displacement of B with respect to A when polariser B is rotated. 

When electromagnetic waves are reflected from a shiny surface, such as a road sign, they often become polarised. 

Suggest how to determine experimentally if visible light reflected from a road sign is polarised.

Changes in phase can also occur when electromagnetic waves are reflected from a surface. 

If an electromagnetic wave is reflected at the boundary between a medium with a higher refractive index than the medium it is travelling in, the oscillating electric field undergoes a phase change of π radians. 

Light is incident on an air-water boundary. A displacement-position sketch of the amplitude of the incident electric field is shown in Figure 1. The origin represents the boundary.

Figure 1

On Figure 1, sketch the amplitude of the reflected electric field.

Three polaroid filters P₁, P₂ and P₃ are aligned as shown in Figure 2. 

Unpolarised light is incident on P₁ and subsequently passes through each of the three polaroid filters. P₁ and P₂ are fixed, but P₃ can be rotated to any angle θ to that of P₁.

Figure 2

Determine the angles of θ at which minima and maxima of emergent light intensity occur.

In the spaces provided in Table 1, state whether the waves listed are polarised or unpolarised, and give a reason for your answer. 

Some of the spaces have been completed for you. 

Table 1

Frequency and wavelength are fundamental properties of all waves. The relationship between them depends on the context of interaction and on the type of wave in question. 

Sketch a graph showing the relationship between the frequency and wavelength of an electromagnetic wave.

Figure 1 shows the variation of air pressure with time of a sound wave.

Figure 1

Sketch on Figure 1 separate graphs to show another sound wave of: 

   (i)         The same loudness but higher pitch. Label this graph X.

   (ii)        The same pitch but quieter. Label this graph Y.

Figure 2a and Figure 2b shows the cross-sections of water waves produced by a plane wave vibration generator in a ripple tank. These waves are measured to move across the ripple tank at 20 cm s^–1, travelling from left to right. 

A small fishing boat is shown on the water surface at O in Figure 2a. The same boat is then shown 0.2 seconds later at O’ in Figure 2b.

Figure 2a

Figure 2b

Calculate the wavelength of the water waves generated by the plane wave vibration generator.

Discuss the motion of the boat during the next 0.2 s. 

State clearly any assumptions you make in your answer.