Module 4 - Section 2 - Superposition And Coherence

Question 1

What is superposition ?

Answer 1

Superposition happens when two or more waves pass through each other - this leads to interference

Question 2

What happens there instant that waves cross ?

Answer 2

At the instant that waves cross - the displacements of each wave ( basically like the amplitudes - amplitudes is just the maximum point of displacement on a wave ) combine - and then after that the waves continue on their own

Question 3

What happens if the 2 waves add up to make a bigger wave ?

Answer 3

Then the waves becomes louder

Question 4

What is the scientific deification of superposition ?

Answer 4

The principle of superposition says that when two or more waves cross, the resultant displacement equals the vector sum of the individual displacements - you can think of the displacements as vectors

Question 5

Whats the simple definition of superposition ?

Answer 5

It’s just when 2 waves pass through each other - meet each other and this gather leads to interference which is when the waves add together

Question 6

What are the 2 types of interference ?

Answer 6

Destructive and constructive interference

Question 7

What is interference ?

Answer 7

When two or more waves superpose each other - pass through each other - the effect of this is called interference

Question 8

Whats constructive interference ?

Answer 8

Some examples of constructive interference:

• A trough plus a trough gives a bigger trough
• a crest plus a crest equals a even bigger crest - vector sum of the displacements

Question 9

Whats destructive interference ?

Answer 9

It’s when a trough plus a crest get added and they equal nothing - the two displacements angle ech other out completely and there is no sound

However if the crest and a trough aren’t the same size then the destructive interference isn’t total - meaning that it doesn’t fully cancel out

Question 10

What has to happen in order for the interference to be noticeable ?

Answer 10

The two amplitudes should be nearly equal

Question 11

What does in phase mean ?

Answer 11

Two points that are in phase with each other if they are both at the same point ion the wave cycle

Question 12

What do waves in phase have in common with?

Answer 12

Waves that are in phase have the same displacement and velocity

Question 13

Whats one complete cycle of a wave equal to ?

Answer 13

One wave cycle ( oscillation ) is equal to 360 degrees or 2pie radians

Question 14

Are waves that have a phase difference of a multiple of 360 degrees or have a phase difference of 0 in phase or out of phase ?

Answer 14

They are in phase

Question 15

Points with a phase difference of odd number multiples of 180 degrees or pie radians are …

Answer 15

Exactly out of phase

Question 16

How can 2 different waves be in phase ?

Answer 16

This is because both waves come from the same oscillator or in other situations - there will nearly always be a phase difference between two waves

Question 17

What does it mean if two sources are coherent ?

Answer 17

If two sources are coherent this means that they have the same frequency and the same wavelength and if they have a fixed phase difference between them

Question 18

What does constant phase difference mean or fixed phase difference ?

Answer 18

It means that between two waves the phase difference is the same for all positions on the waves

Question 19

What is phase difference ?

Answer 19

Phase difference can be defined as the difference between the position of two waves vibrating in the same direction - they don’t rise and fall and the same time

Question 20

Does interference still happen with waves that have different frequencies and wavelengths ?

Answer 20

Yes it does but it happens in a jumble -= in order to get clear interference patterns then the 2 sources must be coherent

Question 21

What does constructive and destructive interference depend on ?

Answer 21

Constructive and destructive interference depends on the path difference

Whether you get constructive or destructive interference at a point all depends on how much father one wave has traveled than the other wave to get to that point - the point at which the waves meet

Question 22

What is path difference ?

Answer 22

It is the amount by which the path travelled by one wave is longer than the path travelled by the other wave

Basically the amount of how much further one wave travelled than the other wave - its the path difference because its the difference between the 2 paths that the waves took - one travelled longer

Question 23

When do you get constructive interference ? Also mathematically ?

Answer 23

You get constructive interference at any point which is equal distance from both sources - so if the point is 5m away from one source and 5m away from the other source

You also get constructive interference when the path difference is a whole number of wavelengths

Maths:

Constructive interference happens when —> path difference = n x wavelength ( where n is an integer - meaning whole number )

Question 24

When does destructive interference happens and also mathematically ?

Answer 24

At times when the path difference is an odd number of half wavelengths then the waves arrives out of phase and you get destructive interference

Maths:

Destructive interference happens when —> path difference = ( n + 1/2 ) x wavelength

Question 25

When does destructive interference happens and also mathematically ?

Answer 25

At times when the path difference is an odd number of half wavelengths then the waves arrives out of phase and you get destructive interference

Question 26

How can you observe interference with sound waves ?

Answer 26

Connect two speakers to the same oscillator so that the waves are coherent - as then it is easier to see interference patterns

Walk slowly across the room in front of them - you will hear varying volumes of sound - at points where the volume is the loudest there is constructive interference which means that the path difference of the 2 waves is pie

And where you hear the quietest sound is where the path difference is an odd number of half-wavelengths - meaning pie / 2