Wave Motion

• WOD are underlined

Wave Motion

• WAVE: A transfer of energy or propagation of a disturbance.

• A wave is the motion of a disturbance

• All waves carry energy and momentum.

Wave Motion• A wave is the motion of a disturbance• Mechanical waves: require

–A medium that can be disturbed–Some source of disturbance, i.e., a

wave generator.

• All waves carry energy and momentum

Transverse Wave

Wave movement is perpendicular to wave propagation. Wave is up and down motion.

Transverse

Longitudinal Wave orCompression Wave

Wave movement is parallel to wave propagation. Demo with Colored Slinky.

To Prof: On Next slide: Show 1. Wave Generator

2. Fixed End3. Reflection

4. Wave and Reflection Add5. Molecules do not propagate,

but only oscilllate.

Longitudinal

• Waves do not move material. • The medium – the material that is “waving”. It

only oscillates. It does not move forward along with the wave.

• MEDIUM DOES NOT MOVE FORWARD.• It stays in place and oscillates.

• Note the blue bobber in the next slide.

Surface waves

• By watching the blue bobber oscillate, it can be seen that a surface wave is a combination of a transverse wave (up and down) and a longitudinal wave (left and right) which produces a SHM in the shape of a circle.

Parts of a wave. They repeat.

1 wave

Ending Node is Starting Node for the next wave.

Waveform – A Picture of a Wave

• The brown curve is a “snapshot” of the wave at some instant in time

• The blue curve is later in time

• The high points are crests of the wave

• The low points are troughs of the wave

Wave Parts:

• Crests: high points

• Troughs: low points

• Nodes: Zeros or Intercepts

New Symbol

• Wavelength: “λ” – Lambda

• The length of the wave

• Distance between identical points on adjacent periods, i.e., crest to crest, trough to trough, or starting node to starting node.

• Measured in meters– Or micrometers or nanometers

In the drawing, one cycle is shaded in color.

The amplitude A is the maximum excursion of a particle of the medium fromthe particles undisturbed position.

The wavelength is the horizontal length of one cycle of the wave.

The period is the time required for one complete cycle.

The frequency is related to the period and has units of Hz, or s-1.

Tf

1

Velocity of a wave

• Remember– λ = distance per cycle– f = cycles per time

• Multiply them together:– λ*f= distance/cycle * cycles/time

Velocity of a wave

• Remember– λ = distance per cycle– f = cycles per time

• Multiply them together:– λ*f= distance/cycle * cycles/time– λ*f= distance/time = velocity

– Velocity of wave: v = f λ

Velocity of a wave

• The velocity of a wave is determined entirely by the medium.

• The frequency of a wave is determined entirely by the source (wave generator).

• The wavelength, λ= v/f

Velocity of a wave

• The velocity of a wave is determined entirely by the medium.

• i.e.,:

• Sound travels at different speeds through water, air, and wood.

Problem

• A Helium-Neon laser has a wavelength of 6.33 *10-7 m, and a frequency of 4.74 * 10 14 Hz. Find the velocity of this laser beam.

Problem

• A Helium-Neon laser has a wavelength of 6.33 *10-7 m, and a frequency of 4.74 * 10 14 Hz. Find the velocity of this laser beam.

• v = f λ = 4.74 * 10 14 Hz * 6.33 *10-7 m

• =

As a sine wave

• A transverse wave can easily be viewed as a sine wave

Longitudinal waves can too.

Areas of high density are calledCompressions.

Areas of low density are calledRarefactions.

Density is a sine wave

Note: The speaker causes compressions in the air, which you ear interprets as sound.

Interference of Waves

Interference of Waves

• Two traveling waves can meet and pass through each other without being destroyed or even altered

• Waves obey the Superposition Principle–Superposition Principle states the

resulting wave is found by adding together the displacements of the individual waves point by point

What’s going to happen?

• Two wave move towards each other

They add up on top of each other

• They add up on top of each other

Afterwards

• The two waves disturbances have no lasting effect on each other

What’s going to happen?

• Two wave move towards each other

They add up on top of each other

• They add up on top of each other

Afterwards

• The two waves disturbances have no lasting effect on each other

Constructive Interference• Two waves, a and b,

have the same frequency.– Are in phase

• The combined wave, c, has the same frequency and a greater amplitude.

Destructive Interference• Two waves, a and b,

have the same amplitude and frequency

• They are half a cycle out of phase

• When they combine, the waveforms cancel

• Wave of same f, out of phase, cancel each other.

Reflection of Waves – Fixed End

• Whenever a traveling wave reaches a boundary, some or all of the wave is reflected

Reflection of Waves – Fixed End

• Whenever a traveling wave reaches a boundary, some or all of the wave is reflected

• When it is reflected from a fixed end, the wave is inverted.

• The shape remains the same, just upside down.

What happens when a wave interferes with its own

reflection?• Sometimes we get standing waves.

• The a string will only allow certain wavelengths to be standing waves because the endpoints need to be nodes,

i.e., the length of the string determines the wavelength for harmonics.

• For a string with two fixed ends, – λ= 2L / n n = 1, 2, 3, 4 …….