Chapter 12 - Waves 2

Question 1

what happens when two waves meet (interference)

Answer 1

when waves meet in phase - constructive interference - maximum amplitudes of both waves are summed
when waves meet in antiphase - destructive interference - maximum amplitude of one wave and minimum amplitude of another are summed

Question 2

what is superposition

Answer 2

when two or more waves pass through each other and the resultant displacement equals to the vector sum of the individual displacements

Question 3

interference meaning and conditions

Answer 3

interference is the effect which occurs when two or more waves superpose with each other.
for clear interference, sources must be coherent - same wavelength and frequency and fixed phase diff

Question 4

Path difference

Answer 4

Path diff between two waves is the difference in the lengths travelled by each wave

Question 5

Path difference and phase difference

Answer 5

Path diff = even multiple of λ/2 : phase diff = multiple of 2π : constructive interference

Path diff = odd multiple of λ/2 : phase diff = odd multiple of π : destructive interference

Question 6

How do path and phase diff increase from the central maxima

Answer 6

Central maxima: path diff = 0 AND phase diff = 0
1st order minima: path diff = 1/2λ AND phase diff = π
1st order maxima: path diff = λ AND phase diff = 2π
2nd order minima: path diff = 3/2λ AND phase diff = 3π
2nd order maxima: path diff = 2λ AND phase diff = 4π

Question 7

double slit experiment process

Answer 7

1. light from lamp passed through a filter to produce monochromatic light (all waves emitted of same frequency)
2. monochromatic light made incident on a single slit, made to diffract and used to illuminate double slit (producing 2 coherent waves)
3. as the light waves from the two slits move forward, they overlap and superpose, producing dark and bright fringes at a screen

Question 8

Explanation for different fringes in Young’s double slit experiment

Answer 8

Bright fringes:
Light waves arrive in phase (even integer π phase diff)
Constructive interference between two light waves (from the two slits)

Dark fringes:
Light waves arrive in anti-phase (odd integer π phase diff)
Destructive interference between two light waves (from the two slits)

Question 9

Double slit experiment equation

Answer 9

λ = ax/D

λ = wavelength of incident light
a = slit separation
x = fringe separation
D = distance between slits and screen

Question 10

What is a stationary wave

Answer 10

A wave formed when two progressive waves, of the same frequency, propagate in opposite directions and superpose.

Question 11

Harmonics

Answer 11

Lowest frequency sound that can be produced on a string of given length, mass and tension is the:
Fundamental frequency, f0 … the first harmonic
The next discrete frequency that can be produced, f1, is the second harmonic e.t.c.
Each harmonic is a multiple of the fundamental frequency:
1st harmonic = 1 x f0
2nd harmonic = 2 x f0

Question 12

Nodes and antinodes of harmonics

Answer 12

[where L is length of string]
1st harmonic: 1 ANTINODE and 2 NODES - λ = 2L
2nd harmonic: 2 ANTINODES and 3 NODES - λ = L
3rd harmonic: 3 ANTINODES and 4 NODES - λ = 2/3 L

Question 13

Nodes and antinodes of harmonics

Answer 13

[where L is length of string]
1st harmonic: 1 ANTINODE and 2 NODES - λ = 2L
2nd harmonic: 2 ANTINODES and 3 NODES - λ = L
3rd harmonic: 3 ANTINODES and 4 NODES - λ = 2/3 L

Question 14

Closed air pipes

Answer 14

Only odd harmonics of the fundamental frequency can form
1st harmonic = 1 x f0
3rd harmonic = 3 x f0
5th harmonic = 5 x f0

Question 15

Open air pipes

Answer 15

Each harmonic is a multiple of the fundamental frequency:
1st harmonic = 1 x f0
2nd harmonic = 2 x f0
3rd harmonic = 3 x f0