Waves

Waves• Wave: an oscillation that moves

from one place to another.– Movement of energy– Sound, light, water waves, radio

waves

• Medium: the material the wave moves through– Sound waves move through air– Water waves move through water– X-rays move through your body

• Waves always move outward

Types of Waves

• Transverse Wave: oscillate perpendicular to the direction the wave moves.

• Longitudinal Wave: vibrate in the same direction the wave moves.

Describing a Wave

• Frequency: the rate that the every point on the wave moves back and forth– Higher frequency, faster it moves

back and forth– # cycles / # seconds

• Amplitude: the maximum amount a wave moves from the equilibrium position– Half the distance from top to

bottom

Parts of a Transverse Wave• Crest: the high point of a wave• Trough: the low point of a wave

• Wavelength (λ): the length of one cycle of a wave– Crest to crest– Trough to trough– Point to point

• How many waves are in the diagram?• What is the λ?

Parts of a Longitudinal Wave

• Compression: compressed portion, high point• Rarefaction: stretched portion, low point

• Wavelength: compression to compression

Wave Interactions

• Boundary: where the conditions or the medium changes.

• When a wave meets a boundary, it does one of four things, which are:– Reflection: the wave bounces and goes in a new direction

– Refraction: the wave bends as it passes into and through an object

– Diffraction: the wave bend around or through holes in an object

– Absorption: the wave is absorbed and disappears

Interference• Interference (superposition): when two or more

oscillations/waves combine (add together)– They are in the same space at the same time

• Constructive Interference: when parts of two waves add together

• Destructive Interference: when parts of two waves cancel each other

Standing Waves

• Standing Wave: a wave that resonates in a confined space

• Nodes: points where the medium does not move

• Antinodes: points in a standing wave that have the greatest amplitude (bumps)

Standing Waves

• Wavelength: length of 1 cycle (2 bumps).

• Harmonics: natural frequencies a medium oscillates at– Numbered by how many

antinodes the wave has– Fundamental: lowest natural

frequency; 1st harmonic; 1 bump; 1/2 λ

Standing Waves• The frequency of each harmonic is a multiple

of the fundamental frequency.

• • The wavelength needs to be determined– 1 wave = 2 antinodes

waves

length

#

Harmonic Frequency

1 12 Hz

2 24 Hz

3 36 Hz

4 48 Hz

harmoniclfundamentaharmonic ff #

Resonance and Energy Transfer

If a driving force is in resonance with another system, there can be a large energy transfer. (shattering wine glass, pushing a kid on a swing, etc)

If the driving force is out of phase with the other system, there can be an energy loss. (noise canceling headphones, etc)

Superposition Practice

Superposition Practice

Standing Waves

• Speed of a wave is the same, no matter the frequency – Only if the medium does not change

Speed of a Wave

• Energy moves in a wave• The medium stays in the same average place• http://phet.colorado.edu/en/simulation/wave-on-a-string

• A wave has a wavelength of 0.25 meters and has a frequency of 20 Hz. Determine the speed of the wave.

• Sound moves at a speed of 340 m/s. If a particular sound wave has a frequency of 800 Hz, what is the wavelength of the sound wave?

Beats

These two different frequencies, when in superposition with each other, created a third wave with it’s own frequency.

Beats

The difference between the two starting frequencies was the frequency of the resulting signal, which had moments of high amplitude once every second (1 Hz) . Those moments of constructive interference are called “beats”.

2 Hz

3 Hz

1 Hz

F1 – F2 = Fb

More Beats

Basic Problems

A 8 Hz sound wave interferes with a 5 Hz sound wave. What is the frequency of the beats you would hear?

How many beats could you count in a minute?

Basic Problems

You have two sets of tuning forks: Small/Large for set A and Medium/Large for set B.

Which set will produce beats at higher frequency? Why?

Which set will produce beats at a longer interval? Why?

Standing Waves and Music

Almost all brass instruments work on the same principle, which is that you vibrate your lips to create a disturbance in the instrument. If the frequency of your lips matches the resonant frequency of the instrument, sound (a musical note) will be produced at that frequency. (demo)

However, in the confined space of the metal tubing, only whole number wavelengths will resonate, so, once you hit the lowest note possible (without changing the valves), it’s possible to hit twice that frequency, three times that frequency etc. as long as you can produce that frequency vibration with your lips. (demo)

Each successive frequency is a whole number multiple of the fundamental frequency.

In music, each whole number multiple of the fundamental frequency is called an “octave.” (demo)

So, the three boxes above show the 1st, 2nd, and 3rd octaves.

By pressing down valves you open or close parts of the metal tubing, thereby reducing or extending the length of the tubes. Longer tubes will produce lower frequency notes.

https://www.youtube.com/watch?v=4HTtlV88rPY