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 fb = 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 = (f1vs)/(vs - v0)
λ increases as it moves away
f2 = (f1vs)/(vs + v0)
In equations:
f1 - frequency of source
f2 - frequency detected
vs - 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
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 fb = 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 = (f1vs)/(vs - v0)
λ increases as it moves away
f2 = (f1vs)/(vs + v0)
In equations:
f1 - frequency of source
f2 - frequency detected
vs - 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