1. 11.7 Properties of Waves – see also lecture notes 11.7

2. Frequency: The number of times the wavelength occurs in one second
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.

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

4. Period, Frequency

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

6. 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

8. WAVE PROPERTIES 11.8 waves transmit energy
There are two types of waves
Transverse
Longitudinal

9. Transverse Waves

11. Compression Waves/Longitudinal Waves

13. Remember the speed of a transverse wave can be calculated using the formula
or in a cord
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

15. 11.11 Reflection and Transmission of Waves

16. Reflection of a eave pulse on a rope lying on a table top
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.

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

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

19. Wave pulse travelling on a string

20. Reflection from a HARD boundary

21. Reflection from a SOFT boundary

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

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

24. 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.

25. 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

26. Phase – The term phase is used to describe the relative position of the wave crests as they meet.
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.

30. 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

31. 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
where n = 1,2,3,…
g. The integer n labels the number of the
harmonic.

32. To find the wavelength,
To find the frequency of each vibration , where n = 1,2,3,…
To find velocity
To find Force of tension

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

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

39. light going from glass to air
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

40. 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

41. 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

42. 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)