Wave Mechanics Physics 1

What is a wave? A wave is: an energy-transferring disturbance moves through a material medium or a vacuum

Categories of Waves Mechanical – require a material medium Medium – state of matter (solid, liquid, gas, plasma) Electromagnetic – can move through empty space (vacuum)

Types of Waves In a transverse wave, the displacement of the particles of the medium is perpendicular to the direction of wave motion.

Types of Waves Transverse Wave

Types of Waves In a longitudinal wave, the displacement of the particles of the medium is parallel to the direction of wave motion.

Types of Waves Longitudinal Transverse l compression rarefaction

Wave Characteristics frequency ( f ) period ( T ) amplitude (A) phase wavelength (l) speed ( v )

1 cycle per second = 1 hertz (Hz) Wave Characteristics The frequency (f) of a wave is the number of complete vibrations (cycles) per unit of time. 1 cycle per second = 1 hertz (Hz)

Wave Characteristics The period (T) of a wave is the time for the completion of a cycle. Measured in seconds.

Wave Characteristics The amplitude (A) of a wave is the maximum displacement of the particles in a medium from equilibrium. (“height from rest to crest”) related to the energy in the wave. Higher amplitude = more energy higher frequency shorter wavelength

Wave Characteristics The phase of a wave describes the position and direction of any particle in a wave-carrying medium.

Wave Characteristics

Wave Characteristics The wavelength (l) of a wave measures the distance between any two consecutive points in-phase.

Wave Characteristics v = d = l = l f t T The speed (v) of a wave depends on the properties of the medium through which it is traveling. v = d = l = l f t T

Electromagnetic Spectrum f f l l

Wave Properties The direction of propagation of the advancing wave is perpendicular to the wave front. This is due the wave property of rectilinear propagation.

Wave Properties fixed end free end

Wave Properties When wave encounters a boundary between two media of different propagation speed, some wave energy can be turned back. This is called the wave reflection.

Wave Properties reflected wave incident wave

Refraction - the bending of a wave caused by a change in speed as the wave moves from one medium to another.

Wave Properties When a wave passes through an opening in a barrier, the wave energy will spread out beyond the barrier. This is called the wave diffraction.

Wave Properties Principle of Superposition - When two waves traveling independently through the same medium, the resultant displacement of any particle at a given time is the vector sum of the displacements that the individual waves acting alone would give it.

Wave Properties When two wave pulses encounter each other in a medium, the wave pulses will superpose beyond the barrier. This is called the wave interference.

Constructive Interference Wave Properties Constructive Interference

Destructive Interference Wave Properties Destructive Interference

Standing Waves A standing wave is the result of two waves of the same frequency and amplitude traveling in the opposite directions through the same medium.

Standing Waves A point of no disturbance in a standing wave is called a node. A point in standing wave where the amplitude is maximum is called an antinode.

Standing Waves The fundamental frequency (or natural frequency) of a medium occurs when it vibrates with the simplest standing wave – 2 nodes + 1 antinode.

Standing Waves The harmonic of a wave is a component frequency of the wave that is an integer multiple of the fundamental frequency. 1st Harmonic = 5 2nd Harmonic = 10 3rd Harmonic = 15 4th Harmonic = 20

Harmonic Series