Intro to Waves

Intro to Waves All things wiggle/vibrate/oscillate. A wave is a wiggle in time. The equilibrium is the resting position of a wave. An object is at rest when experiencing a balance of forces. An object will remain in this position until it is disturbed. Forced vibration: The force which sets the resting object into motion.

Intro to Waves Waves transfer energy without transferring matter. Two types of waves: Mechanical (through a medium) Electromagnetic (through a “vacuum”, an empty space)

Mediums A medium is a substance or material that carries the wave from its source to other locations. The medium consists of particles that interact with each other. Each particle interacts with the adjacent particle, which allows the disturbance to travel through the medium Examples: air, metal, string, people Waves travel at different speeds based on the medium

Mechanical Waves Requires a medium Ex: water, sound, slinky, stadium 2 types: Transverse – particles of the medium move perpendicular to the direction that the wave moves Longitudinal – particles of the medium move parallel to the direction that the wave moves

Wave particles move perpendicular to the direction the wave travels Perpendicular to the direction of travel Direction of travel Transverse Wave: Wave particles move perpendicular to the direction the wave travels Ex: strings of a musical instrument

Particles vibrate parallel to the direction the wave travels Longitudinal Wave: Particles vibrate parallel to the direction the wave travels Ex: sound wave Direction of travel Particles vibrate parallel to the direction of travel

Parts of a transverse wave Crest Wavelength (ג) amplitude Equilibrium Position Wavelength (ג) amplitude Wavelength (ג) Trough

Parts of a Transverse Wave – Sine Curve Crest- highest point on a wave, maximum positive displacement from equilibrium Trough- lowest point on a wave, maximum negative displacement from equilibrium Equilibrium position- resting position Amplitude- from the equilibrium position to the crest or trough Wavelength – distance between any two identical points on a wave

Amplitude Amplitude is a measure of the amount of energy carried by a wave High energy = large amplitude Low energy = small amplitude

Parts of a Longitudinal Wave Compression- point where the particles are closest together Rarefaction- point where the particles are furthest apart

Periodic Motion A wave moves over the same path over the course of time The object not only repeats the same motion, it does so in a regular fashion If it takes 3.2 sec to complete the 1st cycle, it will take 3.2 sec to complete the 2nd, 3rd, 4th… A motion that is regular and repeating is called periodic motion

Damping Some energy is being dissipated over the course of time. The mechanical energy of the vibrating object is lost to other objects. The amount of displacement from its equilibrium position changes slightly with each vibration cycle. Eventually the vibrations will cease.

Pulse vs. Wave Pulse: A single disturbance of the medium particles. The energy passes through the medium in a single cycle and then the disturbance ceases. Wave: A repeated and periodic disturbance of the medium particles. A wave vibrates back and forth over a period of time.

Wave pulse is a single wave disturbance Wave train (continuous wave) - is a series of pulses at intervals

Speed of waves Speed: how fast an object is moving. For a wave, speed is the distance traveled by a given point on the wave, such as the crest, in a given time interval V = d/t Ex: If a crest moves 20 m in 10 sec, what is the speed? V = 20 m/10 s V = 2 m/s

Frequency Frequency (f) is a measure of the number of cycles per unit of time. Measures in hertz (Hz) F = # cycles/time

Wavelength wavelength ( ג ): length of one wave (crest to crest or trough to trough) unit: m (meter)

Problem: What is the velocity of a wave that has a frequency of 3 Hz and a wavelength of 5 m?

Period Period (p) is the time for a particle on a medium to make one complete vibrational cycle. Measured in seconds P = time/# cycles

Frequency and Period Frequency and Period are inversely related P = 1/F F = 1/P If you know one you can solve for the other. P may also be shown as T (time)

Relationship between Frequency and Wavelength Wavelength and frequency are inversely related As frequency goes up the wavelength gets shorter (assuming no change in velocity)

Practice: Example 1: The frequency of a wave is 560 Hz. What is its period? Example 2: A girl floats in the ocean and watches 12 wave crests pass her in 46 s. Calculate the wave: a) frequency b) period Example 3: The period of a wave is 0.044s. How many cycles will the energy source make in 22s?

Wave Boundary Behavior As a wave travels through a medium it will often reach the end of the medium and encounter an obstacle or another medium Boundary – the interface of the 2 media Boundary behavior – the behavior of a wave upon reaching the end of a medium

Wave Interactions Reflection Refraction Diffraction

Wave interactions Reflection: The bouncing back of a wave when it encounters a new medium or boundary Ex: light off a mirror, or sound echo Incident wave- incoming wave Reflected wave – the wave that returns

Reflection Law of Reflection: The angle of incidence is equal to the angle of reflection

Refraction The bending of a wave path as it enters a new medium Caused by difference in speed of the new medium

Diffraction Spreading of waves around edges or through an opening of a boundary

Superposition Displacement of a medium by two or more waves is the sum of the displacements of the waves alone

Interference of Waves Result of the superposition of two or more waves meeting while traveling along the same medium. Constructive- when the wave displacements are in the same direction; amplitudes add Destructive – when the waves have opposite amplitudes; amplitudes subtract Only temporary as paths cross

Constructive interference

Destructive interference

Standing Wave Node Antinode A wave that appears to be standing still Result from the interference between the incident wave and the reflected wave The point of no displacement is the node The point of maximum displacement is the antinode Node Antinode

Electromagnetic wave Move through empty space (no medium) Created by moving electrons Ex. radio waves, microwaves, light