What is a Wave?• A wave is a transfer of energy without a transfer of matter.• Waves can be thought of as any vibration that starts in one place, and moves to another.
Mechanical vs. Electromagnetic Waves• Mechanical waves are the vibrations of a medium.• Mechanical waves need the medium in order to exist, such as sound waves in air or water.
Mediums• The medium is the substance that is waving, as well as the conditions its under.• For example: – Warm air and cold air are different mediums. – A tight guitar string and a loose guitar string are different mediums. – Deep water and shallow water are different mediums.
• Electromagnetic waves are waves that travel without needing a medium to disturb, such as light travelling through the vacuum of space.
Periodic vs. Pulse Waves• If a wave is produced by a regularly repeated motion, the resulting wave is called a periodic wave - a wave which repeats its shape over and over again.• Pulse waves are created by a single disturbance, such as dropping a rock into water.
Transverse Waves• Transverse waves are what we think of when we picture a wave in our heads... a wave that just goes up and down.
Terminology• Crests: high points• Troughs: low points• Rest Position: where the medium would be if there was nothing waving it.• Amplitude (A): the distance from the rest position to a crest or trough• Cycle: one complete piece of a periodic wave• Wavelength (λ): the length of a cycle
• In a transverse wave the particles of the medium move perpendicular to the direction the wave itself.
Longitudinal Waves• Longitudinal Waves are sometimes called compression waves.• They occur any time a medium is compressed.• Since one area in the medium has more matter in it than usual, other areas must have less than usual.
Terminology• Compressions - the areas with extra particles• Rarefactions - the areas missing particles
• In a longitudinal wave, the particles move back and forth parallel to the waves direction.
• Compressions and rarefactions in a longitudinal wave can be compared to the crests and troughs in a transverse waves.• For this reason, longitudinal waves are often represented by transverse waves, since theyre much easier to draw.
• Transverse waves can only be created in a medium where the particles have a bond between them.• If theres no bond, theres no reason for a particle to move just because its neighbour did*.• Example: A guitar string being plucked.*Note: The most obvious type of waves, waterwaves, are a weird case.
Not Attraction = No Transverse Wave Attraction = Transverse Wave
• In a longitudinal wave, particles bump into other particles causing them to move.• No attraction is required.• Example: Sound waves in air.
Frequency & Period• Frequency (f) is the number of cycles that pass a reference point per second.• Technically, "cycles" are unitless, so frequency is just measured in "inverse seconds", or Hertz, (Hz).• 1 Hz = 1/s = 1 s-1
• Period (T) is the amount of time that it takes for one cycle to pass a given point.• Since cycles are unitless, period is just measured in seconds.
• Period and frequency are inversely proportional to each other. T = 1/f f = 1/T
• Example:• While sitting on a beach, you count 30 waves pass by you in 2 minutes.• What is the period and frequency of these waves?
• The period of each wave is... T = 120 s / 30 cycles = 4 s• So the period of these waves is 4 seconds.
• The frequency of the waves is... f = 30 cycles / 120 s = 0.25 s-1 = 0.25 Hz• So the frequency of the waves is 0.25 Hz.
Phase Shifts• Phase shift is just a measure of whether or not 2 (or more) waves are in sync with each other or not.• There are 3 possibilities that have significance to us...
In Phase• The waves are at the same part of their cycles are the same time.• Both have crests at the same time.
Opposite Phase• The waves are at opposite parts of their cycles at the same time.• While one is a crest, the other is a trough.
Out of Phase• This refers to any 2 waves that are not in phase with each other. While it is often taken to mean the same thing as opposite phase, the waves can just by out of sync by a bit.
• A complete cycle can be though of as 360o, just like a circle.• After going through 360o, the pattern repeats itself.
• Here, you can see how the sine and cosine curves are related to a circle, with one complete cycle being 360o.• Note that these are measuring in radians: 360o = 2π ≈ 6.28
• We talk about waves being out of phase by a certain number of degrees.• Here, wave A is 1/4 of a cycle (or 90o) off of wave B.• We say that A is leading B by 90o, or B is lagging A by 90O.