Chapter 6: Combining Waves

Question 1

What is superposition?

Answer 1

When two waves of the same type overlap and interact.
The resultant displacement of the resulting wave is the vector sum of each wave’s displacement.

Question 2

What is interference?

Answer 2

The superposition of waves from two coherent sources.
Constructive if waves are in phase, destructive if waves are in antiphase.

Question 3

What are two coherent sources?

Answer 3

Produce waves of the same type with the same frequency and consistent phase difference.

Question 4

What is path difference?

Answer 4

The difference in distance travelled by two waves meeting at a point.
If it is nλ, constructive interference occurs as the waves arrive in phase.
If it is nλ + 0.5λ, destructive interference occurs as the waves arrive in antiphase.

Question 5

What is Young’s Double Slit Experiment?

Answer 5

The use of two coherent light sources (or one coherent source with a double slit, each slit a coherent source) to produce an interference pattern of bright and dark fringes on a screen.

Question 6

What is the fringe spacing equation (double slit equation)?

Answer 6

w= λD/s
w: fringe spacing
λ: wavelength
s: distance between sources
D: distance between sources and screen
Where D is much larger than w

Question 7

What interference pattern can be seen when white light is used in Young’s double slit experiment?

Answer 7

Central white maxima, other maxima show a spectrum of colours with violet light closest to the 0th order and red light furthest.

Question 8

What causes the interference pattern in Young’s Double Slit Experiment?

Answer 8

The waves from the two coherent sources superposing and interfering with each other.
Where the path difference is nλ, the waves arrive in phase causing constructive interference (bright fringe).
When the path difference is nλ + 0.5λ, the waves arrive in antiphase causing destructive interference (dark fringe).

Question 9

How are fringes ordered?

Answer 9

Central bright fringe is n=0 (0th order) then the closest on either side is n=1, then n=2, etc.

Question 10

What are safety precautions taken when using a laser?

Answer 10

Do not be at eye level to the laser to avoid laser beam entering someone’s eye
Remove reflective surfaces or angle them down to avoid stray reflections entering someone’s eye

Question 11

Why is a laser used in Young’s Double Slit experiment?

Answer 11

Produces monochromatic and coherent light

Question 12

What is a stationary (or standing) wave?

Answer 12

A wave formed by the superposition of two progressive waves of the same frequency and amplitude travelling in opposite directions.

Question 13

How are stationary waves often formed?

Answer 13

When a reflected progressive wave superposes with the original wave.
The reflected wave has a phase change of 180 degrees or pi radians so the waves are out of phase.

Question 14

What is a node?

Answer 14

A point of zero (minimum) amplitude on a stationary wave

Question 15

What is an antinode?

Answer 15

A point of maximum displacement in a stationary wave

Question 16

What is a harmonic?

Answer 16

A mode of vibration that is a multiple of the first harmonic

Question 17

What is the equation for frequency of a harmonic on a string?

Answer 17

f= (1/2L) (√(T/μ))
f: frequency
L: length of string (m)
T: tension in string (N)
μ: linear density of string (kg/m)

Question 18

What is an example of stationary sound waves and waves on a string?

Answer 18

In wind instruments, eg flutes, organs (pipes), or stringed instruments.
At an open end of a tube, there is an antinode where vibration of air particles is greatest. At a closed end of a tube, there is a node where particles cannot vibrate.
On a string, stationary waves form when it is plucked or bowed.

Question 19

What is an example of stationary microwaves?

Answer 19

In microwave ovens, stationary waves often develop causing over-cooked food at antinodes and undercooked food at the nodes, hence a rotating turntable.

Question 20

What is diffraction?

Answer 20

When waves pass through a gap (of similar magnitude to their wavelength) or move past an obstacle, causing them to spread out.

Question 21

What is the diffraction pattern from a single slit?

Answer 21

Central bright fringe (maxima) which has high intensity and double the width of the double-slit central maxima, caused by constructive interference
Has dark regions (minima) and less bright fringes either side (decreasing intensity)

Question 22

What is a diffraction grating?

Answer 22

A grating with hundreds of slits per millimetre

Question 23

How can the central maximum width be increased in a single slit pattern?

Answer 23

Wavelength can be increased, slit width can be decreased.
Causes greater diffraction which causes a larger central maximum.

Question 24

What is the path difference of light from adjacent slits for the 1st order maxima?

Answer 24

λ

Question 25

What angle does light travel at to the direction of incident light?

Answer 25

θ 1

Question 26

What are some applications of diffraction gratings?

Answer 26

Used as part of a spectrometer to investigate atomic spectra. Used to analyse light from galaxies (red-shift).
Used in CDs and DVDs to reflect light rather than transmitting it.

Question 27

What is the equation used for diffraction gratings?

Answer 27

nλ = dsinθ

d: slit separation (m)
λ: wavelength of light (m)
θ: angle between the 0th and nth order maxima
n: order of the maxima

Question 28

What is the difference between the single slit and diffraction grating pattern?

Answer 28

Single slit produces wide central maxima with smaller bright fringes on either side
Diffraction grating produces evenly spaced bright fringes that dim slowly on either side of centre