Chapter 12 - Waves 2

Question 1

What is the principle of superposition

Answer 1

“The principle of superposition states that when 2 waves meet at a point, the resultant displacement at that point is equal to the sum of the displacements of the individual waves”

Question 2

What is constructive interference

Answer 2

Where 2 waves superpose and are in phase and the resultant displacement is greater than the original wave

Question 3

What is destructive interference

Answer 3

Where two waves superpose not in phase and the resultant wave has a smaller displacement than the individual waves

Question 4

What are the conditions required for a constant interference pattern
and how can we remember if path or phase

Answer 4

• constant phase difference
• same frequency

h in coherent therefore h in phase

Question 5

What happens when two waves interfere

Answer 5

• there are maxima where 2 waves constructively interfere
• there are minima where 2 waves destructively interfere
• maxima and minima are caused by 2 waves having different path differences by travelling different distances from their source

Question 6

What are the conditions in terms of path and phase difference for waves to constructively interfere

Answer 6

where n is an integer:
- the path difference must be n(lambda)
- the phase difference must be 2Pi(n)
I.e the waves are in phase, there is a whole wavelength or phase separating them

Question 7

What are the conditions in terms of path and phase difference for waves to destructively interfere

Answer 7

Where n is an integer
- path difference = (n +1/2) x (lambda)
- the phase difference is (2n+1)(pi)
I.e. the waves are not in phase 
They are in antiphase

Question 8

Describe an experiment to test for interference from sound

Answer 8

• play a sound of set frequency through 2 identical and parallel speakers
• record the intensity of the sound using a microphone as you move across the front of the speakers in a straight line

Question 9

How to test for interference in microwaves and deduce wavelength

Answer 9

• set up 2 signal generators producing waves of constant frequency which are coherent
• move an oscilloscope across the front of the experiment and find where the first order maxima is
• measure distance from centre of first slit to first order maxima
• measure distance from centre of second slit to first order maxima
• the difference should be equal to wavelength
• repeat for other maxima and take an average

Question 10

What was the importance of the evidence created by Young’s double slit experiment

Answer 10

• it proved the wave-like nature of light rather than particles
• if particles you would expect no diffraction thus only two bright marks directly in front of slits
• this is not what was observed
• interference patterns were observed

Question 11

How to set up Young’s double slit experiment

Answer 11

• 2 coherent waves are required for an interference pattern
• a monochromatic light source is shone through a double slit
• onto a screen
• the monochromatic light source can be formed using a filter and a single slit

Question 12

What is the formula for a double slit experiment

Answer 12

Lambda = ax/d
Lambda is wavelength
a is the slit separation
x is the distance between maxima
d is the distance of the screen from the slits

Question 13

How does a stationary wave form

Answer 13

• when 2 waves of the same frequency move in opposite directions repeatedly and superpose
• they should ideally be of equal amplitude

Question 14

Where are nodes and antinodes formed

Answer 14

• nodes are formed when the 2 waves are in antiphase and cancel out to form a stationary point of 0 amplitude
• antinodes are formed when the 2 waves are in phase and give a point of max amplitude

Question 15

How to derive wavelength from a stationary wave

Answer 15

The wavelength is equal to twice the distance between adjacent nodes

Question 16

What energy transfer occurs in a stationary wave

Answer 16

There is no net energy transfer, only storage of energy

Question 17

What is the difference between phase difference in progressive and stationary waves

Answer 17

Progressive: the phase changes across a complete wave cycle

Stationary wave: all parts of a wave between nodes are in phase, by nodes they are in antiphase

Question 18

Where L is the length of the string what is the wavelength of the the fundamental frequency

Answer 18

2L

Question 19

What happens when the harmonic increases

Answer 19

F0 = 1 antinodes
F1 = 2 antinodes
F3 = 3 antinodes
F4 = 4 antinodes etc.

Question 20

Can a stationary wave be formed from longitudinal waves

Answer 20

Yes

Question 21

What are the rules of stationary waves in air columns

Answer 21

• always antinodes at open end
• always nodes at closed ends
• From this the wavelength can be calculated

Question 22

What is the equation used for calculating wavelength from a diffraction grating

Answer 22

n(lambda) = a sin(theta)
n = order number
Lambda = wavelength
a = gap separation
Theta = angle to maxima

Question 23

define what a coherent source means

Answer 23

coherent sources are ones of the same frequency and constant phase difference

Question 24

define path difference

Answer 24

the difference in the distance traveled by two separate waves or points on a wave

Question 25

describe three ways stationary waves can be observed

Answer 25

they can be observed through - a string of constant tension and length attached to a vibration generator - water waves bounding off of an end wall and superposing each other - sound waves reflecting off a wall

Question 26

describe the difference in energy transfer between stationary waves and progressive waves

Answer 26

stationary waves simply store energy | progressive waves transfer energy from one place to another

Question 27

describe the difference in wavelength between progressive and stationary waves

Answer 27

in a progressive wave the wavelength is the minimum distance between two parts of a wave oscillating in phase in a stationary wave wavelength is twice the distance between adjacent nodes

Question 28

describe the difference in amplitude between stationary waves and progressive waves

Answer 28

in progressive waves all parts of the wave have the same amplitude over the course of a wave cycle in a stationary wave the amplitude is at its highest in the middle of an antinode and drops back to 0 at a node

Question 29

define what is meant by the fundamental frequency of a wave

Answer 29

the lowest possible frequency for a stationary wave of a given wavelength, usually containing one antinode

Question 30

how to calculate the speed of sound from a resonance tube

Answer 30

- hold a tuning fork above the tube and play a note - change the length if the tube until you hear a loud resonant sound - when the frequency of the resonant sound is equal to that of the tuning fork the length of the tube not in the water is equal to 1/4(wavelength) - from this the speed of the wave can be calculated using the frequency of the tuning fork and 4L

Question 31

graphical methods of analysing young's double slit experiment

Answer 31

- if changing D, plot D (on x) against x (on y), the gradient is lambda/a - if changing a, plot x (on y) against 1/a (on x), the gradient is lambda(D)

Question 32

which direction do the particles vibrate when in a vertical air column with a stationary wave of sound

Answer 32

vertically

Question 33

what equation including sinY can be used for double slit and diffraction gratings

Answer 33

sinY = lambda/ a

Question 34

what equation including tanY can be used for double slit and diffraction gratings

Answer 34

tanY = x/d

Question 35

how do these two trigonometric equations lead to the standard equation for a double slit or diffraction grating

Answer 35

tanY = sinY (approx) where D is much greater than a

Question 36

what other use does the diffraction grating equation have

Answer 36

``` for a known angle you can calculate how many maxima are present lambda = a sinx/n thus n = a sinx/lambda n is maxima number ```

Question 37

what is a stationary wave, define it

Answer 37

a stationary wave is a wave which stores but doesn't transmit energy and is formed of a consistent pattern of nodes and antinodes caused by the interference of progressive waves travelling in opposite directions

Question 38

what is a node

Answer 38

A node occurs where the amplitude/displacement is ALWAYS zero, caused by destructive interference from the superposition of progressive waves

Question 39

what is an antinode

Answer 39

An antinode occurs where the amplitude of the stationary wave takes the maximum possible value, it is caused by constructive interference from the superposition of progressive waves

Question 40

if we have an interference pattern created by EM or sound waves and the electrical inputs to the loudspeakers etc. are reversed what occurs to the interference pattern

Answer 40

- the intensities of the maxima and minima remain the same - there remain the same number of maxima and minima - but their positions are reversed

Question 41

how can we find the wavelength of waves where there is just simple interference (as they travel in the same direction/ not stationary waves) and one speaker is moved

Answer 41

- set the speakers up parallel and emitting the same frequency of waves - slowly move one speaker back until a maxima occurs on a microphone a set distance from the initial position, mark position - continue to move the speaker back until another maxima occurs on the same microphone, mark position - the distance between these two positions is equal to the wavelength