Waves can interfere when they overlap in space. Constructive interference occurs when wave amplitudes add, increasing the overall amplitude. Destructive interference occurs when wave amplitudes subtract, decreasing the overall amplitude. When a wave encounters a boundary, it can be reflected. The angle of reflection is equal to the angle of incidence. Refraction occurs when a wave passes from one medium to another of different density, changing the wave's direction. Standing waves occur when a traveling wave is reflected back on itself, forming areas of maximum and minimum displacement.

1. Interactions of Waves
EQ: How do waves behave?

2. Wave Interference
 Two different material objects can never occupy the same
space at the same time.
 Because mechanical waves are not matter but rather are
displacements of matter, two waves can occupy the same
space at the same time.
 The combination of two overlapping waves is called
superposition.
 Superposition Principle : When two waves interfere, the
resulting displacement of the medium at any location is the
algebraic sum of the displacements of the individual waves
at that same location.
 Works for both longitudinal waves and for transverse waves

3. Wave Interference
 To determine the amount of interference:
 Simplyalign the waves in time and add the
amplitudes
 Amplitudes can be either positive (above
equilibrium) or negative (below equilibrium)

4. Wave Interference
 Constructive Interference:
 If the amplitudes are of the same sign, the
wave is reinforced and grows bigger
 Destructive Interference:
 If the amplitudes are of opposite sign, the
wave is diminished and grows smaller

5. Wave Interference
 Constructive
 Transverse
 Longitudinal
 Destructive
 Transverse
 Longitudinal

6. Wave Interference
 Examples:
 Sound – creates beats
• Constructive = Louder sound
• Destructive = Softer or no sound
 Light
• Constructive = Brighter Light; change in color
• Destructive = Dark or no light
 Water
• Constructive = Larger crests
• Destructive = No visible wave

7. Wave Interference
 Examples:
Interference of two circular
waves. Absolute value
The colors seen in a soap bubble or an oil film snapshots of the (real-
on water are a common example of interference. valued, scalar) wave field.
Light reflecting off the front and back surfaces of Wavelength increasing from
the thin soap film interferes, resulting in different top to bottom, distance
colors being enhanced. between wave centers
increasing from left to right.
The dark regions indicate
destructive interference.

8. Wave Reflection
 Reflection-A wave will bounce off an object
 Wave reflection from surfaces depends on
the characteristics of the surface
 Smooth hard surfaces reflect best
 Rough soft surfaces reflect poorly
 Energy not reflected is absorbed or
transmitted through the material

9. Wave Reflection
 Law of Reflection- A wave bounces off at
the same angle it hits. (angle measured
with respect to the normalline
 Think of arrows pointing in the direction of
the wave motion
Angles Equal

10. Wave Reflection
 What happens to the
motion of a wave when
it reaches a boundary?
 At a free boundary,
waves are reflected.
 At a fixed boundary,
waves are reflected
and inverted.

11. Wave Reflection - Sound
 Echoes are produced
when sound is reflected.
 An echo can only be
heard by the human ear
when the time interval
b/w the echo and the
original sound is greater
than 0.1 s and the
distance b/w the person
and the reflecting surface
is greater than 17 m.
 If smaller than 17 m, then
called Reverberation.

12. Wave Reflection - Examples

15. Wave Refraction
 If there is a change in the characteristics
of a medium, waves are bent
 This occurs because different parts of the
wave front travel at different speeds
 Think of a marching around a curved track
 The inside people have to move more
slowly than the outside people to keep the
lines straight

17. Wave Refraction - Sound

18. Wave Refraction -Light

19. Wave Reflection & Refraction
 The combination of reflection and
refraction enables imaging
 Ultrasonic medical imaging
 Naval SONAR for detecting submarines
 Bats catch mosquitoes

20. Standing Waves
A standing wave is produced
when a wave that is
traveling is reflected back
upon itself.
Appear to stand still
There are two main parts to
a standing wave:
 Antinodes – Areas of
MAXIMUM AMPLITUDE
 Nodes – Areas of ZERO
AMPLITUDE.

21. Standing Waves

22. Standing Waves

23. Natural Frequency
 Objects have ―natural‖ frequencies
 The frequency that they vibrate at when
disturbed
 Based on their size and structure
 Guitar strings are an example

24. Resonance
 Reinforcing of an object’s natural frequency so that
the amplitude increases quickly
 If you have ever been talking in a bathroom and
notice that certain notes are very loud—that’s
resonance: that loud note is the natural frequency
of that room.
 Think about a swing on a playground - You go high
when you pump the swing at its natural vibration
frequency
 Resonance is how a soprano can break a glass
with her voice.

25. Resonance
Tacoma Bridge
7, 1940, one of the most famous incidents
involving the collapse of a bridge occurred.
The Tacoma Narrows Bridge (formerly the
Tacoma Suspension Bridge) was a mile-long
bridge on Route 16 in Washington State. The
original bridge was built with faulty
construction which yielded a potentially
tragic situation when four months after its
completion, the bridge collapsed in the face of
what many recall as a light breeze.
Fortunately, there were no cars on the bridge
at the time of the collapse, hence no human
lives lost. A dog walking on the bridge during
the incident, did in fact lose his life as a result
of the collapse – the light breeze caused the
bridge to “resonate” until the amplitude
became to great for the infrastructure

26. Wave Diffraction
 Diffraction-
is when a wave
spreads out after passing
through an opening.

27. Intensity
 the
energy per unit time per unit area
perpendicular to the direction of wave
propagation.
 Light – Brightness
 Sound – loudness