Chapter 12 - Waves 2

Question 1

What is superposition?

Answer 1

When two waves of the same type meet and overlap to produce a single wave
instantaneous displacement can be found using the principle of superposition of waves

Question 2

What is the principle of superposition of waves?

Answer 2

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

Question 3

What is interference?

Answer 3

When two progressive waves continuously pass through each other and produce a resultant wave

Question 4

What is constructive interference?

Answer 4

When two waves are in phase and the maximum positive displacements line up creating a resultant displacement with increased amplitude

Question 5

What happens to sound and light waves during constructive interference?

Answer 5

Sound waves get louder

Light waves get brighter

Question 6

What is destructive interference?

Answer 6

When two progressive waves are in antiphase, the maximum positive displacement of one wave lines up with the maximum negative displacement of the other wave and the resultant displacement is smaller

Question 7

What happens to sound and light waves in destructive interference?

Answer 7

The sound is quieter and the light is dimmer

Question 8

What happens if two waves with the same amplitude pass through each other?

Answer 8

The resultant wave will have 0 amplitude

Question 9

What is coherence?

Answer 9

When waves emitted from 2 sources have a constant phase difference and have the same frequency

Question 10

What is maxima and minima?

Answer 10

At maxima waves interfere constructively and at minima waves interfere destructively

Question 11

What are the path differences from central maxima to 2nd order maxima?

Answer 11

2nd order maxima - 2 λ
2nd order minima - 1.5 λ
1st order maxima - λ
1st order minima - 0.5 λ
Central maxima - 0

Question 12

What are the phase differences from central maxima to 2nd order maxima?

Answer 12

2nd order maxima - 4π
2nd order minima - 3π
1st order maxima - 2π
1st order minima - π
Central maxima - 0

Question 13

Explain the Young Double Slit Experiment

Answer 13

Two coherent waves are needed for an interference pattern. To show this Young used monochromatic light and a narrow slit to diffract light.

Light diffracting from the single slit arrives at the double slit in phase and diffracts again. Each slit acts as a source of coherent waves which spread from the slit and form an interference pattern with bright and dark fringes.

The experiment was used to determine the wavelengths of various different colours of visible light

Question 14

What is monochromatic light?

Answer 14

A colour filter is used that only allows a specific frequency of light to pass

Question 15

How do you calculate the wavelength of the light used to form an interference pattern?

Answer 15

λ=ax/D

Wavelength = Seperation of slits x seperation of fringes / distance from slits to screen where pattern is observed

only works if a < d

Question 16

What is a stationary wave?

Answer 16

When two progressive waves of the same frequency travelling in opposite directions are superposed.

Question 17

What is a node?

Answer 17

Points where the waves are in antiphase and displacement, amplitude and intensity are 0
Always destructive interference

Question 18

What is an antinode?

Answer 18

When the two waves are in phase and the point where amplitude and intensity are highest

Question 19

What are some properties of stationary waves?

Answer 19

The separation between two adjacent antinodes or nodes is equal to half the wavelength of the original progressive wave.

The frequency is the same as the original waves

There is no net energy transfer

In between adjacent nodes the particles are oscillating in phase however amplitude differs

On different sides of a node the particles are in antiphase.

Question 20

What happens if a string is stretched between two fixed points?

Answer 20

The points act as nodes and when the string is plucked two progressive waves travelling in opposite directions are created that then form a stationary wave.

It vibrates in the fundamental mode of vibration where the wavelength is double the length of the string

Question 21

What is the fundamental frequency?

Answer 21

The minimum frequency of a stationary wave for a string

Question 22

What is a harmonic?

Answer 22

When a string forms other stationary waves at higher frequencies than the fundamental frequency

Question 23

What is the wavelength and frequency at different harmonics for a stationary wave between two points fixed on a string?

Answer 23

1 - f0 , 2L
2 - 2f0 , L
3 - 3f0, 2/3L
4 - 4f0, 1/2L
5 - 5f0, 2/5L

f0= Fundamental frequency
L = Length of string

Question 24

How do you prove that sounds waves bouncing off of a surface can produce a stationary wave?

Answer 24

The waves reflect and travel in the opposite direction superposing.
Connect a speaker to a signal generator and face it towards a wall. Place a microphone connected to an oscilloscope in the middle.

Question 25

How does a stationary wave form in a tube closed at one end?

Answer 25

There must be an antinode at the open end as oscillations are at their greatest and a node at the closed end as the air cannot move at the closed end

Question 26

How do harmonics work in a tube closed at one end?

Answer 26

There is no second harmonic (or multiples of two) and the frequencies are always an odd multiple of the fundamental frequency

For wavelength you do harmonic number /4 λ

3rd harmonic = 3/4 λ