 # Chapter 11:Vibrartions and Waves

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Chapter 11:Vibrartions and Waves
Section 3: Properties of Waves Section 4: Vibrations and Waves

Section 3: Properties of Waves

Wave Motion A wave is the motion of a disturbance.
Ex: Ripples in a pond A medium is the physical environment through which a disturbance/wave can travel. Ex: The pond A mechanical wave is a wave that requires a medium to travel through. Ex: Sound Waves (electromagnetic waves are NOT material waves because they can travel in space)

Wave Types Pulse Wave: a wave that has one pulse.
Periodic Wave: a wave that has continuous pulses. Sine Wave: describe particles that vibrate with simple harmonic motion. Simple Harmonic Motion: any single point on the wave vibrates up and down. Transverse Wave: a wave where the vibrations are perpendicular to the wave motion. -Ex: Light Waves -Crest: the highest point above the equilibrium position. -Trough: the lowest point above the equilibrium position. -Amplitude: distance from equilibrium to crest or trough. -Wave length (λ): distance from crest to crest or trough to trough. Longitudinal Wave: a wave where the vibrations are parallel to the wave motion. -Ex: Sound Waves - Areas that are compressed are density and pressure waves. -Longitudinal Waves can be represented on a waveform (compressed areas are represented by crests and stretched areas are represented by troughs).

Period, Frequency and Wave Speed
Wave Frequency describes the number of waves that pass a given point in a unit of time. Period of Wave describes the time it takes for a complete wavelength to pass a given point.

Equations v= Δx/ Δt v= λ/T f= 1/T v= λ/T = f λ v=f λ v= velocity (m/s)
f= 1/T v= λ/T = f λ v=f λ v= velocity (m/s) Δt= change in time (s) Δx= displacement (m) λ = wavelength (m) T= period of vibration (s) f= frequency (Hz)

Waves transfer energy -The greater the amplitude the more energy
-The energy transferred is proportional to the square of the amplitude. - Damping: the amplitude of wave gradually diminishes over time as its energy is dissipated.

Section 4: Wave Interactions

Wave Interaction -Superposition: The combination of two or more waves.
-The waves Interact to form Interference Pattern

Constructive Interference
Constructive Interference: When the resultant wave is larger than the individual displacements. -The two pulses are traveling towards each other on the same side of the equilibrium position -Superposition Principle- When two or more waves travel through a medium at the same time, the resultant wave is the sum of the displacements of the individual waves at each point. -After the pulses pass each other, they have the same shape and are going in the same direction. -Ex: In a concert, the waves travel in all directions and crash into each other but still maintain their own characteristics.

Destructive Interference
Destructive Interference: When the positive and negative displacements are added, the resultant wave is the difference between the pulses. -The two pulses are traveling towards each other on opposite sides of the equilibrium position -Complete Destructive Interference- When two pulses coincide and the displacements are added, the resultant wave has a displacement wave of zero. -After the pulses pass each other, they have the same shape and are going in the same direction. -Ex: When a compression (particles move together) and a refraction (particles move apart) interfere, there is destructive interference.

Reflection -At a free boundary, waves are reflected.
-The reflected pulse is upright and has the same pulse as the incident (original) pulse -At a fixed boundary, waves are reflected and inverted. -The displacement is in the opposite direction of the original pulse and the amplitude is the same.

Standing Waves -Standing Wave: A wave pattern that results when two waves of the same frequency, wave length, and amplitude travel in opposite directions and interfere -The resultant wave pattern appears to be stationary on the string. -Nodes: Points at which complete destructive interference happen. -Antinodes: The midway point between two adjacent points at which the largest displacement/amplitude occurs. -A standing wave with 2 nodes has a wavelength of 2 times the size between the nodes. (Or 2 times the size of the whole string (L), so 2L) -A standing wave with 3 nodes has a wavelength of 2 times the size between the nodes. (Or 2 times the size of the 1/2 of the string (L), so L) -A standing wave with 4 nodes has a wavelength of 2 times the size between the nodes. (Or 2 times the size of the 1/3 of the string (L), so 2/3L)