Waves 2

Question 1

State the principle of superposition

Answer 1

When two waves meet at a point, the resultant displacement at that point is equal to the vector sum of their individual displacements.

Question 2

In waves, what is interference?

Answer 2

The superposition of coherent waves to produce a resultant displacement.

Question 3

What is the phase difference between adjacent antinodes on a stationary wave?

Answer 3

pi radians

Question 4

Compare progressive and stationary waves in terms of phase difference:

Answer 4

Progressive wave phase changes across one complete cycle, stationary wave all parts of wave between a pair of nodes are in phase

Question 5

What did the Young double slit experiment give evidence for?

Answer 5

The wave nature of light (because interference patterns are formed)

Question 6

What is the separation between adjacent nodes on a stationary wave?

Answer 6

lambda/2

Question 7

How are stationary waves formed?

Answer 7

By two progressive waves of the same frequency travelling in opposite directions (eg by reflection of waves) superposing to form nodes and antinodes

Question 8

For two coherent in-phase wave sources, under what circumstances is a minimum observed at a point?

Answer 8

When the path difference is (n+1/2)lambda, an odd number of half wavelengths, then destructive interference occurs.

Question 9

What is destructive interference?

Answer 9

When two waves are in antiphase, the resultant displacement from the superposition of the two waves has a minimum amplitude.

Question 10

For two coherent in-phase wave sources, under what circumstances is a maximum observed at a point?

Answer 10

When the path difference is nlambda, a whole number multiple of the wavelength, then constructive interference occurs.

Question 11

Define path difference:

Answer 11

The difference in distance travelled to a specific point by two waves from different sources

Question 12

Compare progressive waves and stationary waves in terms of energy transfer:

Answer 12

Progressive waves transfer energy, in stationary waves, there is no net transfer of energy

Question 13

Define coherence

Answer 13

Two coherent waves have a constant phase difference (must be waves of the same type with the same frequency)

Question 14

If two points on a wave (or two waves) are completely in phase what is their phase difference in degrees and in radians?

Answer 14

Zero (or 360degrees or 2pi radians)

Question 15

Define phase difference

Answer 15

The difference in phase between two points on the same wave or between two waves (measured in degrees or radians)

Question 16

Compare progressive waves and stationary waves in terms of wavelength

Answer 16

Progressive waves λ is a minimum distance between two adjacent points oscillating in phase, stationary wave λ is twice distance between adjacent nodes (or antinodes)

Question 17

Compare progressive waves and stationary waves in terms of ampitude:

Answer 17

Progressive wave all parts of the wave have the same amplitude (if no energy loss)
Stationary wave- maximum amplitude at antinodes dropping to zero at node

Question 18

If two points on a wave (or two waves) are in antiphase, what is their phase difference in degrees and in radians?

Answer 18

pi radians, 180 degrees

Question 19

Give the frequency as a multiple of the fundamental and wavelength in terms of length of string for the first five possible harmonics of a stationary wave on a string:

Answer 19

1st harmonic frequency = wavelength = 2L
2nd harmonic frequency = L
3rd harmonic frequency = 2L/3
4th harmonic frequency = L/2
5th harmonic frequency = 2L/5

Question 20

Give the quantities and their units for the equation λ = ax/D

Answer 20

λ = wavelength (m)
a = slit separation (m)
x = fringe spacing (m)
D = distance from the slits (m)

Question 21

Give the wavelength in terms of length of tube for the first five possible harmonics of a stationary in an air column closed at one end:

Answer 21

1st harmonic wavelength = 4L
2nd harmonic wavelength = 4L/3
3rd harmonic wavelength = 4L/5
4th harmonic wavelength = 4L/7
5th harmonic wavelength = 4L/9

Question 22

For air columns in tubes, what must be true for stationary waves at closed and open ends?

Answer 22

Closed end = node (minimum amplitude)

Open end = antinode (maximum amplitude)

Question 23

Describe nodes and antinodes in terms of phase difference:

Answer 23

At nodes waves are in antiphase so undergo destructive interference.

At antinodes, waves are in phase so undergo constructive interference.

Question 24

What is constructive interference?

Answer 24

When two waves are in phase the resultant displacement from the superposition of the two waves has a maximum amplitude

Question 25

Under what circumstances can the equation λ = ax/D be used?

Answer 25

Two sources of monochromatic coherent waves, D»a
(Young double-slit)

Question 26

Give the wavelength in terms of length of tube for the first fives possible harmonics of a stationary wave in an air column open at both ends:

Answer 26

1st harmonic wavelength = 2L
2nd harmonic wavelength = L
3rd harmonic wavelength = 2L/3
4th harmonic wavelength = L/2
5th harmonic wavelength = 2L/5