Module 4: C12 - Waves 2

Question 1

Diffraction Definition

Answer 1

Diffraction is the spreading of waves as they pass through a gap or aperture.

Question 2

Phase Difference Definition

Answer 2

Phase difference tells us how far apart the waves are when comparing their phases (when they’re at their peaks and throughs)

Question 3

Coherent Definition

Answer 3

Waves with the same frequency are coherent

Question 4

Incoherent Definition

Answer 4

Waves with different frequency are incoherent

Question 5

Path Difference Definition

Answer 5

Is the difference between 2 wave paths

Question 6

Superposition Definition

Answer 6

When 2 waves/signals overlap and they add their amplitudes

Question 7

Interference Definition

Answer 7

Interference is the net effect of the combination of two or more wave trains moving on intersecting or coincident paths

Question 8

When does Diffraction happen

Answer 8

Occurs when waves pass through a gap or around an object of roughly the same size or smaller than their wavelength.

Question 9

What happens if there is a larger gap when diffraction takes place

Question 10

What happens if there is a larger gap when diffraction takes place

Answer 10

Large gap - the middle parts of the waves go straight through the gap, with a slight curving at the edges of the waves.

Question 11

What happens if there is a smaller gap when diffraction takes place

Answer 11

Small gap - if the gap is smaller than the wavelength of the waves, the waves fan out in circles.

Question 12

How is diffraction increased when going through a gap and around an obstacle

Answer 12

When going through a gap:
There is more diffraction if the size of the gap is similar to the wavelength

When going round an obstacle:
More diffraction if wavelength is increased (or frequency decreased)

Question 13

How big is one wave cycle in radians

Answer 13

Angle of one rotation = 2π rads (360°)

Question 14

What does Phase Difference mean?

Answer 14

Phase difference means when waves have the same frequency but oscillate differently to each other

Question 15

What does it mean when two waves are “In Phase”

Answer 15

These two waves have different amplitudes but the same frequency and hit their peaks at the same time – they are “in phase”

Question 16

What does it mean when 2 waves are “In Antiphase”

Answer 16

These two waves start opposite to each other – they are “in antiphase” or “out of phase by π radians”

Question 17

What makes 2 waves coherent?

Answer 17

Two waves are said to be “coherent” if they have the same frequency and the same constant phase difference.

Question 18

What is the principle of Superposition?

Answer 18

When two or more waves overlap, the resultant displacement at a point is equal to the sum of the individual displacements at that point. This is the principle of superposition.

Question 19

When will Constructive Interference occur

Answer 19

If both waves have the same sign displacement (i.e. both positive or both negative) constructive interference (reinforcement) will occur.

Question 20

When will Destructive Interference (cancellation) occur

Answer 20

At the point of overlap, if one wave has a positive displacement and the other has a negative displacement, destructive interference (cancellation) will occur.

Question 21

What happens in Constructive Interference

Answer 21

Constructive Interference - when the crests (or troughs) of two waves coincide, they combine to create an amplified wave.

Question 22

What happens in Destructive Interference

Answer 22

Destructive Interference - where the crests of one wave are aligned with the troughs of another, they cancel each other out.

Question 23

Why do interference patterns contain a series of maxima and minima?

Answer 23

In both cases these maxima and minis are a result of the two waves having travelled different distances from their sources. This difference in the distance travelled is called the path difference.

Question 24

How can you find the wavelength of Young’s Double Slit experiment

Answer 24

By considering the dimensions of different parts of a double-slit experiment we can derive a formula to calculate the wavelength λ of the light used to form the interference pattern.

λ = ax / D

Question 25

What experiment did Young use to determine the various wavelengths of the different colours of visible light

Answer 25

Two coherent waves are needed to form an interference pattern. He used a monochromatic source of light and a narrow single slit to diffract the light.

Light diffracting from the single slit arrives at the double slit in phase. It then diffracts again from the double slit. Each slit acts as a source of coherent waves, which spread from each slit, overlapping and forming an interference pattern that can be seen on a screen as alternating bright and dark regions called fringes.

The Young double-slit experiment successfully demonstrated the wave nature of light.

Question 26

Worked Example:

In a Young double-slit experiment, an eyepiece was moved 9.2 mm when measuring the distance from the left edge of the second bright fringe to the left edge of the 12th fringe. The screen is 2.5 m from two slits 1.6 mm apart.

a) What is the wavelength of the light?

Answer 26

λ = ax/D

(12-2)x = 9.2mm => x = 9.2x10^-4m
D = 2.5m
a = 1.6mm => 1.6x10^-3m

λ = (1.6x10^-3 x 9.2x10^-4) / 2.5
λ = 5.9x0^-7m => 590nm

Question 27

Worked Example:

In a Young double-slit experiment, an eyepiece was moved 9.2 mm when measuring the distance from the left edge of the second bright fringe to the left edge of the 12th fringe. The screen is 2.5 m from two slits 1.6 mm apart.

b) The light is replaced with a red laser with wavelength 632 nm. What is the new distance from the left edge of the second bright fringe to the left edge of the 12th fringe?

Answer 27

λ = ax/D

λ = 632nm => 6.32x10^-9 m
D = 2.5m
a = 1.6mm => 1.6x10^-3m

x = Dλ / a
x = (632x10^-9 x 2.5) / 1.6x10^-3
x = 9.9x10^-4m

Question 28

Explain why the central fringe in a Young double-slit experiment is bright?

Answer 28

Because the distance is the centre point on the screen is the same from both of the slits, so the distance travelled by light from slit 1 to the screen is exactly the same as the distance from slit 2 and there is no path difference. This means the waves super pose exactly in phase and constructive interference occurs.

Question 29

Difference between Energy Transfer in a Progressive and Stationary Wave

Answer 29

Progressive Wave:
Energy transferred in the direction of the wave

Stationary Wave:
No net energy transfer

Question 30

Difference between Wavelength in a Progressive and Stationary Wave

Answer 30

Progressive Wave:
Minimum distance between two adjacent points oscillating in phase, for example, the distance between two peaks or two compressions.

Stationary Wave:
Twice the distance between adjacent nodes (or anti nodes) is equal to wavelength of the progressive waves that created the stationary wave.

Question 31

Difference between Phase Difference in a Progressive and Stationary Wave

Answer 31

Progressive Wave:
The phase changes across one complete cycle of the wave

Stationary Wave:
All parts of the wave between a pair of nodes are in phase, and on different sides of a node they are in antiphase

Question 32

Difference between Amplitude in a Progressive and Stationary Wave

Answer 32

Progressive Wave:
All parts of the wave have the same amplitude (assuming no energy is lost to the surroundings)

Stationary Wave:
Maximum amplitude occurs at the antibody then drops to zero at the node.

Question 33

What is a Stationary Wave and how is it produced?

Answer 33

If two progressive waves of the same frequency travel in opposite directions, a stationary (or standing) wave is produced.

Stationary waves are not literally stationary, but in contrast to progressive waves, energy is stored and not transmitted.

Question 34

How is a Stationary Wave Formed?

Answer 34

A stationary wave is not a single wave. It forms when two progressive waves with the same frequency (and ideally the same amplitude) travelling in opposite directions are superposed. As they have the same frequency, at certain points they are in Antiphase. At these points their displacement is always zero, and therefore the amplitude and the intensity are zero. At other points when the two waves are always in phase, an antibody is formed - the point of greatest amplitude and therefore intensity.

Question 35

Do Stationary Waves transfer energy?

Answer 35

As the two progressive waves are travelling in opposite directions, there is no net energy transfer by a stationary wave, unlike a single progressive wave.

Question 36

How is a Stationary Wave made on a string?

Answer 36

If a string is stretched between two points, these points act as nodes. When the string is plucked a progressive wave travels along the string and reflects off its ends. This creates two progressive waves travelling in opposite directions that then form a stationary wave.

When the string is plucked, it’s vibrates in its fundamental mode of vibration, in which the wavelength of the progressive wave is double the length of the string (2L)

Question 37

What other ways can Stationary Waves be formed (without using a string/slinky)

Answer 37

Sound waves reflected off a surface can form a stationary wave. The original wave and the reflected wave travel in opposite directions and superposed.

Stationary sound waves can also be made in tubes by making the air column inside the tube vibrate at frequencies related to the length of the tube. The stationary wave formed depends on weather the ends of the tube are open or closed.

Question 38

What is the fundamental frequency of a wave, and how can other stationary waves called harmonics be formed for a string?

Answer 38

The fundamental frequency f0 is the minimum frequency of a stationary wave for a string. Along with this fundamental mode of vibration, the string can form other stationary waves called harmonics at higher frequencies.

Question 39

For a given string with a fixed tension, how are the frequency and wavelength related

Answer 39

For a given string at fixed tension, the speed of progressive waves along the string is constant. From the equation for progressive waves, v = fλ, you can see that as the frequency increases the wavelength must decrease in proportion. At a frequency of 2f0, the wavelength is half the wavelength at f0

Question 40

How are Stationary waves formed in a tube closed at one end

Answer 40

In order for a stationary wave to form in a tube at one end there must be an antinode at the open end and a node at the closed end. The air at the closed end cannot move, and so must form a node. At the open end, the oscillations of the air are at their greatest amplitude, so it must be an antinode.

The fundamental mode of vibration simply has a node at the base and an antinode at the open end. Harmonics are also possible.

Question 41

Is it possible to form a harmonic at 2f0 (or forth, sixth… harmonic) in a tube closed at one end

Answer 41

Unlike stationary waves on stretched strings, in a tube closed at one end it is not possible to form a harmonic at 2f0 - there is no second (or fourth, sixth…) harmonic in tubes closed at one end are always an odd multiple of the fundamental frequency (3f0, 5f0…)

Question 42

How do Stationary waves in open tubes work (and what harmonics are possible in it)

Answer 42

A tube open at both ends must have an antinode at each end in order to form a stationary wave. Unlike a tube closed at one end, harmonics at all integer multiples of the fundamental frequency (f0, 2f0, 2f0…) are possible in an open tube.

Question 43

Why can closed pipes only produce odd harmonics

Answer 43

Because there must be an antinode at the open end and a node at the closed end a closed pipe can only produce odd harmonics (f0, 3f0, 5f0…)

Question 44

How to measure the speed of sound using a tube, speaker and oscilloscope

Answer 44

•Set a frequency on the signal generator

•Move the microphone out of the tube, until a maximum amplitude (antinode) is seen on the oscilloscope, record this position

•Move it again until the next maximum, record this position.

• Measure the distance between the two antinodes. This is half the wavelength.

• Multiply wavelength x frequency to obtain wave velocity