Waves

What are waves? A wave is a transfer of energy from one place to another. Waves take many forms, but 2 main types. Wave Characteristics include: Amplitude Wavelength Frequency Period Wave Speed

Transverse Waves particles in the medium vibrate perpendicularly to the line of wave speed Examples: water waves, waves on a string wavelength crest amplitude trough

Longitudinal Waves (Compressional Waves) particles in the medium vibrate parallel to the wave velocity made up of alternating areas of high pressure (compressions) and low pressure (rarefactions) Examples: Sound waves, slinky waves compression rarefaction

Mechanical Waves Waves that require a medium to transfer energy. May be either transverse or compressional (longitudinal). Examples: Sound waves, water waves, earthquake waves, waves in a string

Electromagnetic Waves Waves that consist of an electric field and a magnetic field working to propagate it through free space (a vacuum) No medium required Best modeled using transverse waves All EM waves travel at the speed of light, c c = 3 x 108 m/s Examples: light waves, microwaves, ultraviolet, infrared, radar, radio waves, gamma rays, x-rays, etc.

Wave Characteristics

Amplitude Amplitude - the maximum displacement of the medium measured from the rest position. Indicates the amount of energy carried by the wave Crest - highest point on waveform, maximum displacement of medium Trough - lowest point on waveform, maximum displacement of medium

Wavelength The distance between corresponding points on consecutive waves.

Frequency Frequency (f or n) - the number of complete cycles (waves) that pass a given point in the medium in 1 second. Measured in Hertz(Hz). 1 Hz = 1 cycle/sec. stays the same when the wave goes from one medium to another

Period Period (T) - the time it takes for one complete cycle to pass a given point in the medium, or the time that passes before the motion repeats itself. Measured in seconds. f = 1/T T = 1/f

v = lf Wave Speed velocity the wave travels through a medium velocity is determined by the medium v = 3*108 m/s for electromagnetic v = 343 m/s for speed of sound in air v = lf

Standing Waves Caused by a wave and its reflected wave interfering in the medium Wave pattern of alternating nodes and antinodes. Nodes - areas of no displacement of the medium caused by destructive interference Antinodes - areas of maximum displacement of the medium caused by constructive interference. Note: The wavelength of a standing wave consists of 2 antinodes. 1 wavelength is shown. node Antinode

Doppler Effect When the source and the observer are moving at different velocities, the observer “hears” a different frequency (“apparent frequency”). T - toward o P - positive Bottom is Backward f’ = apparent frequency f = actual frequency v = speed of sound (343 m/s ) vo = velocity of observer vs = velocity of source

Doppler Effect – ex. 1 A fire truck is traveling east at 30 m/s, blaring its sirens at 600 Hz. The frantic homeowner is running east at 5 m/s. What frequency does the homeowner hear?

Doppler Effect – ex. 2 Mr. Balch strikes a middle C tuning for (256 Hz) and starts running? The confused (but stationary) band members hear a frequency of 253 Hz. How fast is Mr. Balch running? Which way?

Interference When two or more waves occupy the same space in a medium at the same time they interfere with each other. The medium’s displacement will be the vector sum of the displacements caused by the individual waves. After the waves pass each other they will return to their original forms.

Constructive Interference When two waves interfere in a manner such that the amplitude of the resultant wave is greater than the amplitude of the individual waves.

Destructive Interference When two waves interfere in a manner such that the amplitude of the resultant wave is smaller than the amplitude of the individual waves. Note: Complete cancellation does not always occur in destructive interference.