4.4 Wave Behaviour

K is the source of a wave of frequency 25 Hz.

The wave travels to point M by two routes, K → L → M and K → M. The speed of the wave is 15 m s⁻¹.

What is the path difference between the two waves at M in terms of the wavelength λ of the waves?

The diagram below shows an arrangement used to investigate double slit interference using microwaves.

The diagram below shows the view from above:

The microwaves from the transmitter are polarised. These waves are detected by the aerial in the microwave detector (probe). The aerial is a vertical metal rod.

The detector is moved along the dotted line UY. As it is moved, maximum and minimum signals are detected. Maximum signals are first detected at points V and W. The next maximum signal is detected at the position X.

The distances between each of the two slits, S₁ and S₂ and the microwave receiver when the aerial is in position X are S₁X = 0.3335 m and S₂X = 0.3615 m

Select the three correct reasons that explain why the signal strength falls to a minimum between U and V, and between V and W.

Our fingerprints are made up of a series of ridges on the end of the finger. These ridges can be ‘read’ by electronic devices.

The diagram below shows a certain type of fingerprint detector below, which works by scattering light when pressure is applied to a plastic screen. The ridges of the fingerprint press the plastic film against the glass when the finger is pressed to the screen.

When not in use, the plastic screen and the glass have a small air space between them. The diagram below shows the two possible paths for the light when the finger is pressed down.

Which row in the table correctly describes the properties of the fingerprint detector that cause the bright and dark patches on the image produced by the camera?

A sound source X₁ is positioned w cm to the left of sound source X₂. Both sound sources are y m below the detection line AB. AB runs parallel to X₁X₂ . When a sound detector is slowly moved along the line AB, a maxima is first detected at P, followed by a minima at Q, with another maxima at R and a minima at S. PQRS are all equidistant apart with X₁ S = X₂ S.

Which one of the following is a correct expression for the wavelength of the sound?

A ray of light is incident on a material made from three layers, each having a different optical density, so that in each layer the light travels at a different speed.

• For layer 1: refractive index = n₁ and the speed of light = c₁
• For layer 2: refractive index = n₂ and the speed of light = c₂
• For layer 3: refractive index = n₃ and the speed of light = c₃
• Angle of incidence = i
• Angle of refraction = r

This is illustrated in the diagram below:

Which is the correct expression for c₃, the speed of light in the third layer?

Diamonds are highly valued because of their sparkle. This is caused by total internal reflection, which reflects most of the light that falls onto a cut diamond out of the face we see. Fake gems, called ‘paste’, are often used in jewellery because they are cheaper. However, paste gems sparkle much less than real diamonds.

The diagrams show a possible path of light through a real diamond, and another through a fake.

If:

• n = refractive index;
  • n_d is the refractive index of the diamond
  • n_f is the refractive index of the fake
• v = speed of light
  • v_d is the speed of light in the diamond
  • v­­_f is the speed of light in the fake

Which row in the table contains only statements which must be true?

A double slit interference experiment is conducted using monochromatic light of wavelength λ. The centre of the observed pattern is a bright fringe.

What is the path difference between two waves which interfere to give the second dark fringe from the centre?

A student is investigating the interference of waves. They set up coherent waves produced at points S and T and travel outwards in all directions.

The line XY is halfway between S and T and perpendicular to the joining line S and T. The distance XY is much greater than the distance ST.

Which line or lines would an interference pattern be seen along?

When moving from material A to material B, the direction of a ray of light moves away from the normal. If n_A and n_B are the refractive indices of materials A and B respectively, then which of the following statements is true in this situation?