Waves and Interference

Question 1

What is a wave?

Answer 1

A wave can be described as a periodic, or regularly repeating, ‘disturbance’ that transports energy from one point to another. A field is always necessary to have a wave, but a medium is not. The source of a wave is often an oscillator.

Question 2

What is the amplitude, A of a wave?

Answer 2

This is the height of the wave from its equilibrium position.

Question 3

What is the wavelength, λ?

Answer 3

This is the distance from the peak of one wave to the next wave.

Question 4

What is the period, T of a wave?

Answer 4

This is the time it takes for a single wavelength to pass a fixed point.

Question 5

What is the frequency, f of a wave?

Answer 5

This is the rate at which waves pass a fixed point.

f = 1/T

Question 6

What is the wavenumber, k?

Answer 6

This is a value that is given by the formula

k = 2π / λ

Question 7

How to calculate wave speed?

Answer 7

Fora. travelling wave the frequency f, wavelength λ and speed v are related by

v = fλ

Question 8

What is a transverse wave?

Answer 8

This is a wave where the particles of the medium oscillate perpendicular to the direction of travel.

Question 9

What is a longitudinal wave?

Answer 9

This is a wave where the particles of the medium oscillate in the direction of propagation. (slinky like)

Question 10

What are two types of seismic waves and what type of wave are they?

Answer 10

• Primary waves (P wave) - These are the fastest waves, typically felt first after an earthquake. These are longitudinal waves and can travel through solids and liquids.
• Secondary waves (S waves) - these are the slower waves that are felt after the P wave. They are transverse waves and cannot pass through liquid, i.e., the outer core.

Question 11

What is Inertia?

Answer 11

This is measured by the mediums density, for example, mass per unit volume for a waves in a liquid or mass per unit length for waves in a string.

Question 12

What is restoring force?

Answer 12

This depends on the medium and the type of wave. For example, for small ripples on water the restoring force is surface tension, while for large deep water waves the restoring force is gravity. For sound waves it is the change in pressure as the air is compressed and rarefied. For waves on a string, the restoring force is tension in the string.

Question 13

Calculating the speed of a material wave

Answer 13

v = sqrt(F_T / μ)

Where F_T is the tension and μ is the linear density.

Question 14

What are wavefronts?

Answer 14

These are lines (in 2 dimensions) or surfaces (in 3 dimensions) that connect points in a wave that have the same phase. They are perpendicular to the direction of wave propagation at every point.

Question 15

What is reflection?

Answer 15

This is the change in direction of a wavefront at an interface between two different media such that the wavefront stays in the medium from which it originated.

Question 16

What is The law of reflection?

Answer 16

this states that the angle of incidence is always equal to the angle of reflection.

i = R

(where both angles are measured from the normal)

Both the incident ray and the reflected ray must be in the same plane.

Question 17

What is refraction?

Answer 17

This is the change in direction of wavefronts as they pass from one media to another of a different refractive index.

Question 18

What is a refractive index?

Answer 18

This is a number, represented as n, that shows the ratio of the speed of light in a vacuum to the speed of light in the selected medium.

n = c / v

(Refractive indexes are always greater than or equal to one)

Question 19

What is the angle of incidence and the angle of refraction and how are they related mathematically.

Answer 19

The angle of incidence, i, is the angle of the incoming ray measured from the normal.

The angle of refraction, r, is the angle of the ray once it has passed into the new medium and is measured from the normal.

They are related by Snells Law.

Question 20

What is dispersion?

Answer 20

This is where wavelengths of different frequency travel at different speeds through the same medium.

Wave with a higher frequency tend to travel slower than waves of a lower frequency.

Question 21

What is the critical angle?

Answer 21

This is the angle of incidence at which the angle of refraction becomes 90°. Going past the critical angle then allows for total internal reflection.

Question 22

What is total internal reflection?

Answer 22

This is when the angle of incidence has gone past the critical angle when a wave is passing from a media with a higher refractive index to a media with a slower refractive index, then over all of the energy of the wave is reflected back into the slower media (larger refractive index).W

Question 23

What is the principle of superposition?

Answer 23

The principle of superposition states that if two or more waves overlap at a point in space, the resulting disturbance at any point is the sum of the disturbances due to the individual waves.

Question 24

What is a standing wave?

Answer 24

This is the superposition of two waves that are travelling in opposite directions.

Question 25

What are **nodes**?

Answer 25

These are a property of standing waves that occur every half wavelength where the displacement is always 0.

Question 26

What are **antinodes**

Answer 26

These are points of maximum vibrational amplitude halfway between each node.

Question 27

What is **constructive interference**?

Answer 27

This is when the crests and troughs coincide and the waves add up to give a stronger resulting amplitude. Waves can be travelling in the same direction.

Question 28

What is **destructive interference**?

Answer 28

This is where the crests and troughs of two waves so not coincide and the resulting amplitude is less than either of the two waves. Waves can be traveling in the same direction.

Question 29

What is **coherence**?

Answer 29

Two waves can be said to be coherent if: - both waves have the same wavelength, and - the phase relationship between the two waves does not vary with time.

Question 30

What is the **criteria for constructive interference**?

Answer 30

This occurs between waves from two coherent sources at a point in space if the path length difference at a point from the source is an integer number of wavelengths.

Question 31

What is the **criteria for destructive interference**?

Answer 31

This occurs between waves from two coherent sources at a point in space if the path length difference at that point from the wave source is a half integer number of wavelengths.

Question 32

What is the difference in irradiance pattern from the double slit experiment and from a diffusion grating?

Answer 32

- The double slit experiment produces wider peaks from a sinusoidal curve. -A diffraction grating produces a wave with much thinner peaks. creating thinner peaks.

Question 33

What is a **diffraction grating**?

Answer 33

A diffraction grating is a grating that has many very closely, but evenly spaced slits, creating thinner peaks in the **interference pattern**.

Question 34

What is **irradiance**?

Answer 34

This is the power per unit area of the electromagnetic radiation falling on a surface. Bright fringes correlate to high irradiance, and dark fringes correlate to low irradiance.

Question 35

What is the **resolving power** of a diffraction grate?

Answer 35

This a measure of hoe narrow a wavelength range can be reliably measured within the broader range of wavelengths that make up the irradiance pattern.

Question 36

What is the difference between a interference pattern and a diffraction pattern?

Answer 36

An interference pattern is created when the light from two sources interact with one another. Whereas a diffraction pattern can occur from a single light source and is due to secondary waves interacting with each other creating the interference pattern. (They are really very similar physical phenomena)