Waves

A WAVE IS A DISTURBANCE THAT CARRIES ENERGY THROUGH MATTER OR SPACE.

LONGITUDINAL WAVE - Particles vibrate parallel to the direction of the wave. TRANSVERSE: TRANSVERSE WAVE - Particles vibrate perpendicular to the direction of the wave.

Transverse & Longitudinal Wave Animation: http://sites.google.com/site/physicsflash/home/transverse Longitudinal: http://sites.google.com/site/physicsflash/home/sound

Defining Terms Amplitude (A): maximum displacement from equilibrium. Period (T): time it takes to execute a complete cycle of motion Frequency (f): number of cycles or vibrations per unit of time * Unit: Hz = sec-1

Defining Terms Medium: material through which a disturbance travels. Mechanical wave: a wave whose propagation requires a medium. Non-mechanical wave: a wave whose propagation does not require a medium.

Defining Terms Wave Pulse: a single non-periodic disturbance. Periodic wave: a wave whose source is some form of periodic motion. Standing wave: wave pattern that results when two waves of the same f, , and A travel in opposite directions and interfere.

WAVE ANATOMY

Formulas Where: V = wave velocity  = wavelength (m) f = frequency (Hz or sec-1) T = Period (sec)

Sample Calculation 1 The string of a piano that produces the note middle C vibrates with a frequency of 264 Hz. If the sound waves produced by this string have a wavelength in air of 1.30 m, what is the speed of sound in air? Given: f = 264 hz  = 1.30 m v = ? v = f v = (264 Hz)(1.30 m) v = (264 sec-1)(1.30 m) v = 343 m/s

Sample Calculation 2 What is the period of vibration for an x-ray with a frequency of 3.0 x 1012 MHz? (note: MHz is a mega hertz. Mega or M = 106) Given: f = 3.0 E12 MHz = 3.0 E18Hz T = ? T = 1/f T = 1/(3.0 E18 sec-1) T = 3.3 E-19 s

Sample Calculation 3 A tuning fork produces a sound with a frequency of 256 Hz. The speed of sound in water is 1500 m/s. Calculate the wavelength produced by this tuning fork in water. Given: f = 256 Hz v = 1500 m/s  = ? v = f  1500 m/s = (256 s-1)()  = 5.9 m

Wave speeds The speed of a wave depends on it’s medium. The speed of sound in 0oC air is 331 m/s The speed of sound through 100oC air is 386 m/s

The same is true of a wave on a string The same is true of a wave on a string. The speed of the wave depends on the tension in the string (F). the linear density of the string (the mass of string per unit length) ()

Another Formula Where: v = velocity F = Tension (N)  = linear density of the string (kg/m)

Interference CONSTRUCTIVE INTERFERENCE: any interference in which waves combine so that the resulting wave is bigger than the original waves. DESTRUCTIVE INTERFERENCE: any interference in which waves combine so that the resulting wave is smaller than the largest of the original waves.

See Applet groups http://www.aplusphysics.com/courses/regents/waves/regents_wave_interference.html http://mysite.verizon.net/vzeoacw1/wave_interference.html Good for beats http://www.acoustics.salford.ac.uk/feschools/waves/super2.htm http://sites.google.com/site/physicsflash/home/path Scroll down, beats are at the middle/bottom! http://www.acoustics.salford.ac.uk/feschools/waves/super3.htm

Standing Waves STANDING WAVE: a wave form caused by interference that appears not to move along the medium and that shows some regions of no vibration (nodes) and other of maximum vibration (antinodes).

Example of Wave Interference Poor Radio Reception even though close to Transmitter Great Radio Reception!

Reflection Reflection: when a wave bounces back off a boundary. The incoming wave is the incident wave The outgoing wave is the reflected wave. Incident Reflected

Free End Reflection Pulse reflection from a free end: The loop is free to move upward on the pole. Then the downward component of the tension in the string makes the loop go back down creating the reflected pulse. The pulse is reflected back exactly as it came in.

Fixed End Reflection Pulse reflection from a fixed end: As the pulse hits the wall, the pulse pushes up on the wall. The wall then must push back on the rope (Newton’s 3rd law). This causes the pulse to invert. The pulse is reflected back exactly as it came in, only inverted.

See Phet - Waves on a String