Simple Harmonic Motion of a Transverse Wave

A wave is a single vibratory disturbance of energy as it propagates through a medium.

A pulse is a single disturbance.

A pulse on a rope. This is an example of a transverse pulse. As the energy travels to the right the wave is displaced vertically.

Simple Harmonic Motion of a Transverse Wave

• Transverse Wave.

As a transverse wave is generated its motion of travel is perpendicular to wave generation.

Notice: as the wave travels to the right the displacement of the wave is up and down.

Longitudinal wave

A longitudinal wave is generated parallel to wave direction.

A wavelength is the distance between compressions or rarefactions.

A longitudinal wave needs a medium to travel. It will not travel through space.

Amplitude and Wavelength (λ)

Amplitude is the height of the wave from equilibrium position. It represents the loudness or brightness of the wave.

Wavelength is the length of one wave. Crest to crest or trough to trough, etc…

Frequency

• The number of vibrations (waves) per second.

• It is measured in Hertz.

Frequency

• The number of vibrations (waves) per second.

• It is measured in Hertz.

• What is the frequency of a record player rotating at 30 rotations per minute?

Frequency

• The number of vibrations (waves) per second.

• It is measured in Hertz.

• What is the frequency of a record player rotating at 30 rotations per minute?

• 30 rotations / 60 seconds = .5 HZ

Period

• The time for 1 wave to pass a given point.

• The formula: T = 1/f

Period

• The time for 1 wave to pass a given point.

• The formula: T = 1/f

• What is the period of a record player with a frequency of 0.5 Hz?

• T = 1/0.5 Hz

Period

• The time for 1 wave to pass a given point.

• The formula: T = 1/f

• What is the period of a record player with a frequency of 0.5 Hz?

• T = 1/0.5 Hz

• T = 2 seconds

In Phase or Out of Phase?

Speed of the Wave

• The speed of the wave can be calculated by v = fλ or by v = d/t

• Calculate the speed of a wave with a frequency of 6 Hz and a wavelength of 4 meters.

• v = fλ

• v = (6Hz)(4m)

• v = 24 m/s

Diffraction

• The spreading of a wave behind a barrier.

Numerical approximation of diffraction pattern from a slit of width four wavelengths with an incident plane wave. The main central beam, nulls, and phase reversals are apparent.

Note: the areas that look blurry are areas of destructive interference.

Constructive InterferenceThe adding together of waves to make a larger wave.

Destructive interference

• The adding together of two waves as they pass through each out which ends up with a smaller wave. The green line is what you would see.

Wave interference producing constructive and destructive waves

Standing Wave <sw>

A standing wave is formed when two waves traveling in opposite directions with the same frequency, amplitude and speed.

Basically the antinodes are constructive and the nodes are completely destructive.

Double slit interferenceλ/d = x/L

λ is the wavelength of the light source

d is distance between slits

x is the distance between the central maximum and the first order bright band.

L is the length to the screen

Single slit diffraction pattern.

λ is the wavelength of the light and W is the width of the slit.

Fraunhofer Single Slit

Comparisons between double and single slit diffraction.

• If you increase the λ what happens to the distance between the bright spots?

• Single : Increase Double: Increase• If you increase the distance to the screen what

happens to the distance between the bright spots?

• Single : Increase Double: Increase• If you increase the size of the opening what

happens to the distance between the bright spots?

• Single : Decrease Double: Decrease