11.7 Properties of Waves – see also lecture notes 11.7

Frequency: The number of times the wavelength occurs in one second.
Measured in kilohertz (Khz), or cycles per second. The faster the sound source vibrates, the higher the frequency.
Higher frequencies are interpreted as a higher pitch. For example, when you sing in a high-pitched voice you are forcing your vocal chords to vibrate quickly.

Higher amplitudes are interpreted as a higher volume - hence the name "amplifier"
.
for a device which increases amplitude
Sine wave
Amplitude: The strength or power of a wave signal. The
"height" of a wave when viewed as a graph

Wavelength: The distance between any point on a wave and the equivalent point on the next phase. Literally, the length of the wave.

How are frequency and wavelength related?
Electromagnetic waves always travel at the same speed (299,792 km per second). This is one of their defining characteristics. In the electromagnetic spectrum there are many different types of waves with varying frequencies and wavelengths. They are all related by one important equation: Any electromagnetic wave's frequency multiplied by its wavelength equals the speed of light.
FREQUENCY OF OSCILLATION x WAVELENGTH = SPEED OF LIGHT

There are two types of waves a. Transverse b. Longitudinal

Transverse Waves

Compression Waves/Longitudinal Waves

Remember the speed of a transverse wave can be calculated using the formula v
  f or in a cord v

F m
L
The speed of a longitudinal wave has a form similar to that for a transverse wave.
In a long solid rod - where E is the elastic modulus (sec 9.5) and r the material density
In liquid or gas it is written with b the bulk modulus (sec 9.5) and r the material density

11.11 Reflection and Transmission of Waves

Reflection of a eave pulse on a rope lying on a table top. (a) The end of the rope is fixed to a peg. (b) The end of the rope is free to move.

When a wave pulse traveling to the right along a thin cord
(a) Reaches a discontinuity where the rope becomes thicker and heavier, then part is reflected back and part is transmitted (b)

Incident Wave – The wave that strikes a boundary
Reflected Wave – The remaining energy not transferred from the incident wave that is reflected back.

Wave pulse travelling on a string

Reflection from a HARD boundary

Reflection from a SOFT boundary

From low speed to high speed (high density to low density)

From high speed to low speed (low density to high density)

11.12 Interference; Principle of Superposition
Interference – occurs when two waves pass through the same region of space at the same time. The resulting displacement of the waves as they meet is the algebraic sum of their separate displacements.
A crest is considered to have a positive value and the trough negative.

The Principle of Superposition – can best be described as the overlapping wave that is created when two waves meet.
Three types of interference are; a. Constructive Interference b. Destructive Interference c. Partially Destructive

Phase – The term phase is used to describe the relative position of the wave crests as they meet.
a. In phase – results in an amplitude that is the sum of both crests b. Out of phase – occurs when the crests do not meet together and the waves partially or completely cancel each other.
This complete cancellation occurs when a trough of one wave meets the crest of another.

11.3 Standing Wave; Resonance a. Standing wave – produced when two waves interfere such that they produce one large amplitude of constructive interference called the antinode and areas of destructive interference called nodes.
b. The nodes and antinodes will remain in fixed positions for a particular frequency.
c. Because standing waves can occur at more than one frequency, the lowest frequency give rise to a pattern and are known as the natural frequency or resonant frequencies of the cord

d. Fundamental frequency - corresponds to one antinode note the relationship of length to wavelength.
e. Overtones – are the other natural frequencies for the vibrating cord.
and are whole number multiples of the fundamental frequency and are called harmonics.
f. In general we can write the equation
L
 n

2 n where n = 1,2,3,… g. The integer n labels the number of the harmonic.

To find the wavelength,
 n

2 L n
To find the frequency of each vibration , where n = 1,2,3,… f n
 v
 n
 v n
2 L
 nf
1
To find velocity v

F m
L
To find Force of tension
F
T
 mv
2
L

Off a plane surface : Note direction of propagation gets reversed.
This is based on angle of incidence = angle of reflectionθ₁ = θ₂

What happens when a light wave hits glass?
Some is always reflected

Refraction
Occurs when a wave passes from one region to another where it moves at a different speed e.g. light going from air to glass light going from air to water light going from glass to air water waves going from deep to shallow sound waves going from air to solid

At the interface, the frequency will be the same on both sides and v₁ = f λ₁ v₂ = f λ₂
Hence the refracted wave will have a shorter wavelength
Obviously
λ₁ = v₁ λ₂ v₂

Note that the refracted wave is bent since the wavelength is decreased so obviously λ₂ = n₁λ₁ n₂
This gives rise to Snell's law, when the wave hits the interface at an angle

Wave is incident at θ₁. Refracted wave is at θ₂, what is the relation between θ₁ and θ₂?λ₁ = d sin(θ₁) λ₂ = d sin(θ₂) and n₁λ₁ = n₂ λ₂ giving n₁ sin(θ₁) = n₂ sin(θ₂)

http://www.kettering.edu/~drussell/Demos/reflect/reflect.html
http://www.physics.carleton.ca/~watson/1000_level/Waves_an d_Optics/1004_waves.html