SPH3U - Unit 4 - Waves and Sound

Vibration - The cyclical motion of an object about an equilibrium point
Mechanical Wave - The transfer of energy through a material due to vibration
- Medium - The material that permits the transmission of energy through vibrations
- The nature of the medium dictates the actual speed (particle spacing, forces between particles)
Waves - Disturbances that carry energy and cause particles to vibrate
- The particle will eventually return to its original position

Waves can be transverse or longitudinal
- Transverse Wave - A wave in which particles vibrate perpendicular to the direction of the flow of energy
  - ex. light, electromagnetic waves
- Longitudinal Wave - A wave in which particles vibrate parallel to the direction of the flow of energy
  - ex. sound
  - Can’t travel through liquids
  - Compression - The region in a longitudinal wave in which the medium’s particles are closer together
  - Rarefaction - The region in a longitudinal wave in which the medium’s particles are farther apart
Amplitude - The maximum height of the wave from equilibrium position
Wavelength - The distance between a point on one wave and the same point of the next wave
- Represented by λ
Period - The time for a vibrating particle to complete one cycle
- Represented by T
Frequency - The number of complete cycles that occur in a unit of time
- Measured in hertz, or Hz (one cycle per second)
- Represented by f
- f = 1/T
Phase - The x-coordinate of a unique point of the wave in a continuous wave
- The relative displacement of two waves at the same time
- In Phase - The state of two identical waves that have the same phase shift
- Out of Phase - The state of two identical waves that have different phase shifts

Wave Speed - The rate at which a wave in travelling through a medium; also a measure of how fast the energy in the wave is moving
- Represented by v, and measured in distance/time
- v = λf
Factors affecting wave speed
- v = √(Tension/Linear Density)
- Temperature - Increase in temperature causes an increase in motion and a faster wave
- Density - Decrease in density increases wave speed, as they are easier to move
- Tension - Increase in tension causes an increase in speed, as it transmits energy faster
- Linear Density - The mass per unit distance of string
  - The mass divided by length
  - An increase in linear density will decrease the speed

Human hearing ranges from 20 Hz to 20,000 Hz
- Sound waves with a frequency higher than 20,000 Hz are ultrasonic
- Sound waves with a frequency lower than 20 Hz are infrasonic
The speed of sound in air is 330m/s
- Contingent on altitude (sea level) and temperature (20 degrees)
- To calculate varying temperatures:
  - 331.4 + 0.606T, where T is temperature
Mach Number - The ratio of the airspeed of an object to the local speed of sound
- Mach = (speed of object)/(local speed of sound)
Sound Intensity - The amount of sound energy being transferred per unit area
- Related to the air pressure
- Pressure = Force/Area
  - Measured in N/m², or Pascals (Pa)
- Loudness is also related to the amount of energy carried by the wave
  - Loudness is measured in Watts/m² or on the logarithmic decibel (dB) scale

Interference - The process of generating a new wave when two or more waves meet
- When waves interact
- Interference doesn’t affect the properties of the waves
Superposition - At any point the amplitude of two interfering waves is the sum of the amplitudes of the individual waves
- Constructive Interference - The process of forming a wave with a larger amplitude when two or more waves combine
- Destructive Interference - The process of forming a wave with a smaller amplitude when two or more waves combine
- The waves must be in phase

In a free-end, the waves are reflected in phase
In a fixed end, the waves are reflected out of phase
At boundaries that are neither fixed nor free ends:
- When moving from a slower medium to a faster medium, the transmitted and reflected wave will be in phase
- When moving from a faster medium to a slower medium, the transmitted wave will be in-phase, and the reflected wave will be inverted

Standing Wave - A wave created by interference of waves that have the same amplitude and wavelength that appears to be stationary
- The wave from the source interacts with the wave from the boundary
- A pattern of nodes (no vibrations) and antinodes (maximum vibrations) form
Fundamental Frequency - The lowest frequency that can produce a standing wave in a given medium
Harmonics - Whole-number multiples of the fundamental frequency
If both ends are fixed, the ends act as nodes, and there will always be one less antinode than nodes
- For the first harmonic, there are two nodes and one single wave
- This occurs at the natural frequency, or f₀
- L = (nλ)/2
If one end is fixed, the end is a node
- This takes place in an air column
- The first harmonic is a quarter of the wavelength, and every harmonic after is an additional half
- L = [(2n-1)/4](λ)

Beat - Periodic change in sound intensity caused by the interference between two nearly identical sound waves
- This creates a tone whose volume changes
The frequency at which the volume changes is equal to f_b = f₁ - f₂
As the frequency difference increases, the beat frequency increases

Damping - A reduction in the amplitude of a wave as a result of energy absorption or destructive interference
Resonant Frequency - The frequency at which a medium vibrates most easily
- If a wave is constant at the resonant frequency, it will reach the maximum amplitude
Resonance - The condition in which the frequency of a wave equals the resonant frequency of the wave’s medium

Doppler Effect - When a source of waves approaches an observer, the observed frequency of the waves increases; when the source moves away from an observer, the observed frequency of the wave decreases
- In sound - moving towards is a higher pitch, and moving away is a lower pitch
- In light - moving towards is blue/violet, and moving away is red
λ decreases as it moves closer
- f₂ = (f₁v_s)/(v_s - v₀)
λ increases as it moves away
- f₂ = (f₁v_s)/(v_s + v₀)
In equations:
- f₁ - frequency of source
- f₂ - frequency detected
- v_s - speed of sound
- v₀ - speed of object
The effect is also observed when the source of the waves is stationary and the observer is moving