Waves

The Nature of WavesWhat is a mechanical wave?

A wave is a repeating disturbance or movement that transfers energy through matter or space

Each wave carries energy

Requires matter to travel through MEDIUM

Created when a source of energy causes a vibration to travel through a medium

Types of Mechanical Waves

• Transverse wave = a wave that causes the medium to vibrate at right angles to the direction in which the wave travels.

• Line: Rest position• Crest = the highest point of the wave above the rest position• Trough = the lowest point of the wave below the rest position• Ex: S waves in earthquakes

Types of Mechanical Waves• Longitudinal wave = a wave in which the vibration of the

medium is parallel to the direction in which the wave travels

• Compression = an area where particles in a medium are spaced closer together

• Rarefaction = an area where the particles in a medium are spread out

• Ex: springs, primary (P) waves in earthquakes

Wavelength (λ)= the distance between a point on one wave and the same

point in the next cycle of the wave– For a transverse wave: measured between adjacent

crests or adjacent troughs

Wavelength(λ)

• For a longitudinal wave: measured between adjacent compressions or rarefactions

Amplitude= the maximum displacement of a medium from its rest position

– For a transverse wave: the distance from the rest position to a crest or trough

• The more energy a wave has, the greater the amplitude!

Amplitude– For a longitudinal wave: maximum displacement of a point from its

rest position• The more energy a wave has, the more the medium will be

compressed!

Frequency & Period

• Period = the time required for one cycle, a complete motion that returns to its starting point

• Frequency = the number of complete cycles in a given time; for a wave, the # of wave cycles that pass a point in a given time – Unit: hertz (Hz) = cycles per second– A wave’s frequency equals the frequency of the vibrating source

producing the wave

Mathematically, the period is the reciprocal of the frequency and vice versa. In equation form, this is expressed as follows.

Velocity

= the speed of a wave– Velocity = wavelength x frequency– Units: meters/second (when wavelength is in meters

& frequency in hertz)– For waves travelling at a given speed, wavelength is

inversely proportional to frequency. – Velocity is usually constant, unless the wave enters a

new medium or if variables such as pressure/temperature change.

Phase= describes how far to the left or right a wave shifts

Interference= occurs when 2 or more waves overlap & combine

together

• Constructive Interference = occurs when two or more waves combine and their displacements add together; increases amplitude

• Destructive Interference= occurs when two or more waves combine & their displacements are subtracted from each other; decreases amplitude

Reflection

= occurs when a wave bounces off a surface that it cannot pass through

Reflection• When the wave pulse hits a fixed boundary (a

wall) the wave is reflected back.

**Incoming waves are known as incident waves.

A pulse reaching the end of a medium becomes inverted whenever it either:

(1) reflects off a fixed end,(2) or is moving in a less dense medium and reflects off a more dense medium.

Reflection• If the wave is reaches the boundary for its medium and is

entering a new medium (air to water, or air to object, etc.):– Part of the wave is reflected back– Part of the wave is transmitted to the new medium

(1)The transmitted pulse (in the more dense medium) is traveling slower than the reflected pulse (in the less dense medium).(2)The transmitted pulse (in the more dense medium) has a smaller wavelength than the reflected pulse (in the less dense medium).(3)The speed and the wavelength of the reflected pulse are the same as the speed and the wavelength of the incident pulse..

• The transmitted pulse (in the less dense medium) is traveling faster than the reflected pulse (in the more dense medium).

• The transmitted pulse (in the less dense medium) has a larger wavelength than the reflected pulse (in the more dense medium).

• The speed and the wavelength of the reflected pulse are the same as the speed and the wavelength of the incident pulse.

Refraction= the bending of a wave as it enters a new medium

at an angle.– When a wave enters a medium at an angle, refraction

occurs because one side of the wave moves more slowly than the other side.

Diffraction= the bending of a wave as it moves around an

obstacle or passes through a narrow opening

**The larger the wavelength is compared to the size of an opening or obstacle, the more a wave diffracts.

Electromagnetic Waves

= transverse waves consisting of changing electric fields and changing magnetic fields– Produced by a vibrating electric charge and as such,

they consist of both an electric and a magnetic component

– Carry energy from place to place– Vary in wavelengths & frequencies– Can travel through a vacuum or through matter

Electromagnetic Spectrum

= full range of frequencies of electromagnetic waves