4.3 Wave Characteristics

Two coherent sources, A and B, which are in phase with each other, emit microwaves of wavelength 40.0 mm. The amplitude of waves from source B is twice that of source A. 

A detector is placed at the point P where it is 0.93 m from A and 1.19 m from B. The centre axis is normal and a bisector to the straight line joining A and B. 

With reference to the phase of the microwaves, deduce the magnitude of the detected signal at P and explain your reasoning.

Determine the ratio of the intensity at P to the intensity at O.

Discuss, with suitable calculations, what happens to the detected signal as the detector is moved from P to O.

The source B is altered such that it emits waves that are 180° out of phase with source A. 

Deduce the type of interference that now occurs at point P and explain your reasoning. 

Transverse, sinusoidal progressive waves of wavelength λ have points P and Q which are apart. 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, being transverse, can be polarised. A light source is viewed through two pieces of polarisers, A and B, with their axes initially at radians from each other:

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. 

A common incorrect way of drawing this graph is as:

State the differences between the correct graph in part b, and then, through derivation of Malus' Law, explain why the graph above is incorrect.

Plane polarised electromagnetic waves are incident on an aerial positioned to give a maximum response. High winds cause the aerial to rotate about the direction of the incident wave until it makes and angle of 40° to the plane of polarisation.

Calculate the percentage reduction in the amplitude of the signal received by the aerial following the high winds.

The intensity of incident radiation is 0.05 mW m⁻². When the aerial is repaired, it is found to have a maximum vibration amplitude of 6.3 mm.

Determine the angle at which the aerial has been set.

Superposition occurs when two or more waves interfere with each other.

   (ii)      Sketch a diagram to support your answer to part (i).

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Superposition is often demonstrated using water waves which are transverse and clearly show increases and decreases in amplitude.

Describe how sound waves can also undergo superposition.

Two microwave transmitters are placed 15 cm apart and connected to the same source. A receiver is placed 70 cm away and moved along a line parallel to the transmitters. The receiver detects and alternating pattern of maxima and minima.

Explain how the maxima and minima are formed.

One transmitter is removed and a metal grille is placed between the transmitter and the receiver. The grille is rotated through 180^o and back round again. The signal at the receiver is heard to rise and fall as the grill rotates.

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         (ii)         Sketch a graph to show the pattern of rising and falling signal.

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Distinguish between light which is polarised and unpolarised.

Outline the function of an analyser when investigating polarised light.

The analyser is used to investigate polarised light. Light with intensity 11.94 W m⁻² is incident on a polarising filter. The transmission axis of the analyser is fixed at an angle of 35º to the electric field of the polarised light.

(i)        Write down the intensity of the light transmitted by the polarising filte

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    (ii)        Calculate the intensity of the light transmitted by the analyser

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The analyser is rotated through 180^o.

Sketch a graph to show the variation of intensity I₂ with angle θ of the light leaving the analyser.

A microwave transmitter is set up 75 cm away from a receiver which is connected to an oscilloscope so that the intensity of the wave incident on the receiver can be determined.

Initially the intensity is found to be 32 mW m⁻². The receiver is moved to a new position 125 cm from the transmitter. The new intensity is found to be 11.6 mW m⁻². 

Show that these results support the theory that intensity is related to distance according to an inverse square law.

The transmitter remains at 125 cm and the energy of the signal is increased. The new intensity is found to be 46.4 mW m⁻².

Determine the factor by which the energy was increased.

Radio waves are emitted from a straight conducting rod antenna such that the plane of polarisation of the waves is parallel to the rod. An identical metal conducting rod, known as an aerial, is used for reception.

Suggest why the receiving aerial must be set up parallel to the transmitting antenna.

The receiving aerial is moved so that it leans 22^o from its original position. The power of the received signal in the new position is 15 μW.     

A group of hikers are exactly equidistant between two radio transmitters, X and Y. The transmitters are set to an operating wavelength of 200 m and have the same power outputs.

The hikers at point P receive a signal with zero amplitude. Outline what information about the signal you can assume from this.

The hikers walk towards point Q on the line shown and continue to receive a signal of zero amplitude.

Once at Q they turn and walk towards Y, continuing until they receive a signal with amplitude double that emitted from either transmitter.

(i)         Explain why there is no increase in amplitude detected on the walk from P to Q

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(ii)        Calculate the distance they walked along the line from Q to Y

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The hikers continue moving from Q towards the transmitter at Y where the distance QY is 20 km. The signal continues to rise and fall as they walk.

Calculate how many times they will hear the signal fall in intensity as they walk.

The hikers are wearing polarising glasses to protect their eyes from glare.

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