Chapter 11: Waves

Question 1

1. Define progressive waves.
2. Give an example of a progressive wave.
3. Describe the movement of particles when a progressive wave travels through a medium.

Answer 1

1. A progressive wave is an oscillation that travels through a medium or in a vacuum as energy is transferred.
2. Sound is an example of a progressive wave: sound waves vibrate in a plane parallel to the direction of energy transfer as the wave passes through air.
3. The particles in the medium move from their original equilibrium position to a new position. The particles in the medium exert forces on each other.
   A displaced particle experiences a restoring force from its neighbours and it is pulled back to its original position.

Question 2

1. Define transverse wave.
2. What are peaks and troughs in a transverse wave?
3. Give three examples of transverse waves.

Answer 2

1. In a transverse wave, the oscillations are perpendicular to the direction of energy transfer (i.e. as the wave moves from left to right, the oscillations are up and down).
2. Transverse waves have peaks and troughs where the oscillating particles are at max displacement from their equilibrium positions.
3. Transverse waves include waves on the surface of water, electromagnetic waves, and S-waves produced in earthquakes.

Question 3

1. Define longitudinal waves.
2. Define compressions and rarefactions.

Answer 3

1. In longitudinal waves, the oscillations are parallel to the direction of energy transfer.
2. A compression is a region in a longitudinal wave where the particles are closest together. A rarefaction is region in a longitudinal wave where the particles are farthest apart.

Question 4

1. Define ​displacment.
2. Define amplitude.
3. Define wavelength.
4. Define a period of oscilliation.
5. Define frequency.
6. Define wave speed.

Answer 4

1. Displacement, measured in m, is the distance fom the equilibrium position in a particular direction; a vector.
2. Amplitude, measured in m, is the max displacement fro the equilibrium position (can be positive or negative).
3. Wavelength, measured in m and signified by λ, is the minimum distance between two points in phase on adjacent waves.
4. A period of oscillation, measured in s and signified by symbol T, is the time taking for one oscillation or for one whole wavelength to move past a given point.
5. Frequency, measured in Hz is the number of wavelengths passing a given point per unit time.
6. Wave speed, measured in m s^-1 and signified by symbol v [or c], is the distance travelled by the wave per unit time.

Question 5

What is the wave equation?

Answer 5

The wave equation related frequency f in Hz, the wavelength λ in metres, and the wave speed v in m s^-1.

v = f λ

Question 6

What is the relationship between frequency and period?

Answer 6

Frequency f and period T are reciprocals of each other.

Question 7

Describe the concept of phase difference.

Answer 7

• Phase difference describes the diference between the displacements of particles along a wave, or the difference between the displacements of particles on different waves.
  
  • Phase difference is measured in degrees or radians, with each complete cycle or wave representing 360˚ or 2π rad.

Question 8

Describe the phase difference between two particles that are oscillating perfectly in step with each other. What does this mean?

Answer 8

• If particles are oscillating perfectly in step with each other (they both reach their max positive displacement and max negative displacement at the same time) then they are described as in phase.
• They have a phase difference of 0.

Question 9

Describe the phase difference of two particle completely out of step with each other. What does this mean?

Answer 9

• If particles are completely out of step with each other (one reaches max positive displacement as other reaches max negative displacement) then they are described as being in antiphase.
• They have a phase difference of 180˚ of π rad.

Question 10

What does phase difference depend on?

Answer 10

Phase difference depends on the separation of particles in terms of the wavelength.

Question 11

What is the wave profile of a wave? What can this be used to determine?

Answer 11

• The wave profile of a wave is a graph showing the displacement of the particles in the wave against the distance along the wave.
  
  • The wave profile can be used to determine the wavelength and amplitude of transverse and longitudinal waves.

EXAM NOTE: The wave provile changes shape over time.

Question 12

What is a displacement-time graph used to show? What can be determined easily from this graph?

Answer 12

• A displacement-time graph can be used to show how the displacement of a given particle of the medium varies with time as the wave passes through the medium (or itself for electromagnetic waves).
• This graph looks the same for both transverse and longitudinal waves.
  
  • This can be used to determine the period T and amplitude of both types of wave.

Question 13

Describe the phenomena of reflection.

Refer to the law of reflection and changing wave properties.

Answer 13

• Reflection occurs when a wave changes direction at a boundary between two different media, remaining in the original medium.
• The law of reflection states that the angle of incidence is equal to the angle of reflection, and applies whenever waves are reflected.
• When waves are reflected their wavelength and frequency do not change.

Question 14

Describe the phenomena of refraction.

Refer to its definition, partial reflection, angle of refraction, and the effect refraction has on wave properties.

Answer 14

• Refraction occurs when a wave changes direction as it changes speed when it passes from one medium to another.
  
  • Whenever a wave refracts, there is always some reflection off the surface (partial reflection).
• If the wave slows down, it will refract towards the normal. If the wave speeds up it refracts away from the normal.
• Unlike reflection, refraction does have an effect on the wavelength of the wave. If the wave slows down, the wavelength decreases and the frequency remains unchanged (and vice versa).

Question 15

Describe the refraction of sound waves and electromagnetic waves from air to a denser medium.

Answer 15

• Sound waves normally speed up when they enter a denser medium.
• Electromagnetic waves normally slow down when they enter a denser medium.

Question 16

Describe the refraction of water waves in different depths of water.

Answer 16

• The speed of water waves is affected by changes in the depth of the water, which can be used to investigate refraction of water waves.
• When a water wave enters shallower water, it slows down and the wavelength gets shorter.

Question 17

1. Describe the phenomena of diffraction.
2. When are diffraction effects most significant? Explain.

Answer 17

1. Diffraction is a property unique to waves. When waves pass through a gap or an obstacle, they spread out.
   
   • All waves can be diffracted. The speed, wavelength, and frequency of a wave do not change when diffraction occurs.
2. Diffraction effects are most significant when the size of the gap or obstacle is about the same as the wavelength of the wave.
   
   • This is why sound diffracts when passing through a doorway, allowing you to hear conversations around the corner.
   • However, light has a much smaller wavelength, so the diffraction of light can only be observed across a much smaller gap.

Question 18

Describe the phenomena of polarisation.

Answer 18

• Polarisation means that the particle oscillate along one direction only, which mean that the wave is confined to a single plane.
• A plane polarised wave is a wave that oscillates in only one plane: the plane of oscillation.

Question 19

Why is it possible to polarise some waves but not others? Use examples.

Answer 19

• Light from an unpolarised source, like a filament lamp, is made up of oscillations in many possible planes. As light is a transverse wave, these oscillations are always at 90˚ to the direction of energy transfer.
• In longitudinal waves, the oscillations are always parallel to the direction of energy transfer, so longitudinal waves cannot be plane polarised; their oscillations are already limited to one plane.

Question 20

Describe the phenomena of partial polarisation.

Answer 20

• When transverse waves reflect off a surface, they become partially polarised.
• This means there are more waves oscillating in one particular plane, but the wave is not completely plane polarised.
• Some sunglasses contain polarising filters. These only allow light oscillating in one plane to pass through them, reducing the glare reflected off flat surfaces like lakes.

Question 21

How is the intensity of a progressive wave defined?

Answer 21

• The intensity of a progressive wave is defined as the radiant power passing through a surface per unit area.
• Intensity has units watts per square metre (W m^-2) and can be calculated using the equation
  I = P / A
  where I is the intensity of the wave at a surface, P is the radiant power passing through the surface, and A is the cross-sectional area of the surface.

Question 22

1. Describe the relationship between intensity and distance for a point source of a wave.
2. Define a new equation for calculating the intensity, using the area of a sphere.
3. What important relationship does this new equation show?

Answer 22

1. When a wave travelts out from a source, the radiant power spreads out, reducing the intensity.
   For a point source of a wave, the energy and power spread uniformly in all directions.
2. The total radiant power P at a distance r from the souce is spread out over an area equal to the surface area of a sphere (A=4πr²). Substituting this area into the equation for intensity gives
   I = P / A = P / (4πr²).
3. The equation shows that the intensity has an inverse square relationship with the distance from the source:
   ​I ∝ 1 / r².
   
   • For example, if the distance doubles, the intensity is reduced by a factor of four.

Question 23

Describe the relationship between intensity and amplitude.

Answer 23

• As waves travel across a distance, the intensity drops as the energy becomes more spread out. This causes a drop in amplitude, as amplitude is determined by the energy of the wave.
• Decreased ampltidue means a reduced average speed of the oscillating particles.
  
  • As E = 0.5mv², halving the amplitude results in particles oscillating with half the speed and hence, a quarter of the kinetic energy. So the relationship is
    intensity ∝ (amplitude)².

Question 24

Describe how electromagnetic waves are different from longitudinal waves.

Answer 24

• Electromagnetic waves do not need a medium to travel through, unlike all other waves, so they can travel through a vacuum.
• EM waves can be reflected, refracted and diffracted (like all waves).
• EM waves are transverse waves (oscillate perpendicular to direction of motion), so they can be plane polarised.
• All EM waves travel at the same speed through a vacuum (denoted by c), 3.00 x 10⁸ m s^-1. This value is usually used for the speed of light in air.

Question 25

What is the definition of an EM wave?

Answer 25

An EM wave is transverse wave with oscillating electric and magnetic field components.

Question 26

State the EM spectrum.

Answer 26

Question 27

Explain any overlaps in the EM spectrum.

Answer 27

• The wavelength ranges of X-rays and gamma rays overlap.
• Unlike other parts of the spectrum, these EM waves are not classified by their wavelength, but by their origin.
  
  • X-rays are emitted by fast-moving electrons, wheras gamma rays come from unstable atomic nuclei.

Question 28

How are EM waves classified?

Answer 28

The different types of EM waves are classified primarily by wavelength.

Question 29

Are all EM waves naturally polarised?

Answer 29

Most naturally occurring EM waves are unpolarised. The electric fiel oscillates in random planes, all at 90˚ to the direction of energy transfer.

Question 30

How can unpolarised EM waves be polarised?

Answer 30

• Unpolarised EM waves can be polarised using filters called polarisers.
• The nature of the polariser depends on the type of EM wave, but each filter only allows waves with a specific orientation through.

Question 31

Describe one use for the polarisation of EM waves.

Answer 31

• One use for the polarisation of EM waves is in communications transmitters.
  
  • In order to reduce interference between difference transmitters, some transmit vertically plane polarised waves and others nearby transmit horizontally plane polarised waves.

Question 32

Describe the basis of refractive index.

Answer 32

• Different materials refract light by different amounts. The angle at which the light is bent depends on the relative speeds of light in the material.
• Each material therefore has a refractive index, which is calculated using the equation n = c / v, where n is the refractive index of the material (no units), c is the speed of light through a vacuum (3.00 x 108 m s^-1), and v is the speed of light through the material in m s^-1.
  
  • ​The greater the refractive index, the more light entering the material is refracted towards the normal.

Question 33

Describe refraction law.

Answer 33

Question 34

What is total internal reflection?

Answer 34

The total internal reflection (TIR) of light occurs at the boundary betwee two different media.

• When the light strikes the boundary at a large angle to the normal, it is totally internally reflecyed. All of the light is reflected back into the original medium. There is no light energy refracted out of the original medium.

Question 35

Describe the conditions required for total internal reflection.

Answer 35

Two conditions are required for TIR:

• The light must be travelling through a medium with a highest refractive index as it strikes the boundary with a medium with a lower refractive index.
  
  • For example, TIR is possible when glass meets air, but not the other way around.
• The angle at which the light strikes the boundary must be above the critical angle.

Question 36

Describe what happens when the angle at which light strikes the boundary is exactly equal to the critical angle.

How can this be used to deduce an equation for the critical angle?

Answer 36

• When the angle at which the light striked the boundary is exactly equal to the critical angle, the light is not internally reflected and instead travels along the boundary between two media.