Interactions of Waves

EQ: How do waves behave?

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

Wave Interference

Simply align the waves in time and add the

amplitudes

Amplitudes can be either positive (above

equilibrium) or negative (below equilibrium)

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

Wave Interference

Constructive

Transverse

Longitudinal

Destructive

Transverse

Longitudinal

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

Wave Interference Examples:

The colors seen in a soap bubble or an oil film

on water are a common example of interference.

Light reflecting off the front and back surfaces of

the thin soap film interferes, resulting in different

colors being enhanced.

Interference of two circular

waves. Absolute value

snapshots of the (real-

valued, scalar) wave field.

Wavelength increasing from

top to bottom, distance

between wave centers

increasing from left to right.

The dark regions indicate

destructive interference.

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

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

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.

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.

Wave Reflection - Examples

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

Wave Refraction - Sound

Wave Refraction -Light

Wave Reflection & Refraction

The combination of reflection and

refraction enables imaging

Ultrasonic medical imaging

Naval SONAR for detecting submarines

Bats catch mosquitoes

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.

Standing Waves

Standing Waves

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

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.

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

Wave Diffraction

Diffraction- is when a wave

spreads out after passing

through an opening.

Intensity

the energy per unit time per unit area

perpendicular to the direction of wave

propagation.

Light – Brightness

Sound – loudness