Waves and acoustic wave mechanics
Wave Characteristics
What is a wave?
A wave is disturbance that travels through a medium from one location to another location.
Medium - What carries the wave, the material
What is a wave?
A wave is disturbance that travels through a medium from one location to another location.
Medium - What carries the wave, the material
Continuous wave - A succession of individual oscillations or a series of wave pulses
Wave Pulse - An individual oscillation
*There is one critical difference between oscillation and wave motion: whereas oscillation involves no net movement, but merely
movement in place, the harmonic motion of waves carries energy from one place to another.
Parts of the Wave
Crest - Top of the wave
Trough - Bottom of the wave
Wavefront - Parts of the wave that are moving together. (when a rock drops into a pond a circular shape formed by all the waves that
were created at that moment for the wave front)
Ray - The ray highlights the direction of energy transfer
Longitudinal: (look next page for the picture)
Compression - Point where theres high pressure, everything bunched together
Rarefaction - Point where there is low pressure, everything is far apart
Types of Waves:
Transverse - When the motion of the medium is perpendicular to the direction of the wave. (Wave goes left or right, medium goes up
or down)
Wave Pulse - An individual oscillation
*There is one critical difference between oscillation and wave motion: whereas oscillation involves no net movement, but merely
movement in place, the harmonic motion of waves carries energy from one place to another.
Parts of the Wave
Crest - Top of the wave
Trough - Bottom of the wave
Wavefront - Parts of the wave that are moving together. (when a rock drops into a pond a circular shape formed by all the waves that
were created at that moment for the wave front)
Ray - The ray highlights the direction of energy transfer
Longitudinal: (look next page for the picture)
Compression - Point where theres high pressure, everything bunched together
Rarefaction - Point where there is low pressure, everything is far apart
Types of Waves:
Transverse - When the motion of the medium is perpendicular to the direction of the wave. (Wave goes left or right, medium goes up
or down)
Longitudinal - When the motion of the medium is parallel to the direction of the wave. (Wave goes left or right, medium goes left or right)
Transverse waves propagate in solid because solid particles have an equilibrium position where they are pulled back to. While its
being pulled out of its equilibrium position it pulls the neighbor particles and thus create the wave.
Transverse Waves cannot propagate in gas because gas particles do not have an equilibrium position. They are held freely only
binded by the average distance it has to maintain with one atom and the other.
Definitions:
Displacement (x) - Distance in meters that the particle moves from its original position.
Amplitude (A) - The maximum displacement from the original position. The amplitude is only constant if it doesn’t lose any energy.
Period (T) - The time it takes to go through one complete oscillation. Measured in seconds
Frequency (f) - The number of oscillations that take place in 1 second. Measured in Hertz Hz
Wavelength (λ) - The shortest distance between two crests beside each other. (or any two points that are in the same "step" as
the other as in same position but different times) In meters.
being pulled out of its equilibrium position it pulls the neighbor particles and thus create the wave.
Transverse Waves cannot propagate in gas because gas particles do not have an equilibrium position. They are held freely only
binded by the average distance it has to maintain with one atom and the other.
Definitions:
Displacement (x) - Distance in meters that the particle moves from its original position.
Amplitude (A) - The maximum displacement from the original position. The amplitude is only constant if it doesn’t lose any energy.
Period (T) - The time it takes to go through one complete oscillation. Measured in seconds
Frequency (f) - The number of oscillations that take place in 1 second. Measured in Hertz Hz
Wavelength (λ) - The shortest distance between two crests beside each other. (or any two points that are in the same "step" as
the other as in same position but different times) In meters.
Wave speed (v) - The speed in m/s that the wave fronts pass a stationary observer.
Intensity (I) - Power per unit area that is received by the observer. Average energy carried by the wave. Measured in W/m2
*The intensity of a wave is a proportional to the square of its amplitude: I ∝ A2
Period and Frequency are inversely related!!
I = 1/f
f = 1/I
Graphs:
These two don’t specify if it's Transverse or Longitudinal
The displacement - time graph represents the oscillation for one point on the wave.
Every point oscillates at the similar manner, but they start at different times
From this graph we can measure or approximate the period of the wave and the amplitude of the wave at the position of
measurement.
Intensity (I) - Power per unit area that is received by the observer. Average energy carried by the wave. Measured in W/m2
*The intensity of a wave is a proportional to the square of its amplitude: I ∝ A2
Period and Frequency are inversely related!!
I = 1/f
f = 1/I
Graphs:
These two don’t specify if it's Transverse or Longitudinal
The displacement - time graph represents the oscillation for one point on the wave.
Every point oscillates at the similar manner, but they start at different times
From this graph we can measure or approximate the period of the wave and the amplitude of the wave at the position of
measurement.
The Displacement - position graph works like a snap shot of all the points at one instant. From this graph we can measure the
wavelength and the amplitude at given points.
wavelength and the amplitude at given points.
Wave Equations: Relationship between wave speed wavelength and frequency
The Period: time it takes for one complete oscillation
During 1 period the wave pattern will have moved by one wavelength.
*Note f = 1/T
The Period: time it takes for one complete oscillation
During 1 period the wave pattern will have moved by one wavelength.
*Note f = 1/T
Wave Properties
Reflection - The change of direction of a wave when it bounces off a medium.
Refraction - The change in direction of a wave while it goes from one medium to the next. This happens because of the change in speed of the wave as it goes through a new medium
Reflection - The change of direction of a wave when it bounces off a medium.
Refraction - The change in direction of a wave while it goes from one medium to the next. This happens because of the change in speed of the wave as it goes through a new medium
Law of Reflection
Angle i = r1
The original wave is partially reflected and partially transmitted.
The wavelength is smaller in the refracted ray if the speed is reduced.
Angle i = r1
The original wave is partially reflected and partially transmitted.
The wavelength is smaller in the refracted ray if the speed is reduced.
SNell's law
Law of Refraction
The constant is equal the ratio of the different speeds in the different media.
The constant is equal the ratio of the different speeds in the different media.
V1/ V2
Diffraction - The tendency of waves to spread out when they go through an opening or around obstacles.
Diffraction - The tendency of waves to spread out when they go through an opening or around obstacles.
The diffracted wave is as if a new wave started at the point where the opening is at with a circular wave.
A wave will go straight if the aperture is much larger than the wavelength
Wavelength and aperture have to be in the same order of magnitude for it to be noticeable
A wave will go straight if the aperture is much larger than the wavelength
Wavelength and aperture have to be in the same order of magnitude for it to be noticeable
Interference
Interference happens when two waves of the same type meet and a resulting wave occurs.
The resulting wave can be found by using the principle of superposition
Principle of Superposition - The resulting displacement of the medium at any location is the sum of the displacements of the individual waves at that same location.
Interference happens when two waves of the same type meet and a resulting wave occurs.
The resulting wave can be found by using the principle of superposition
Principle of Superposition - The resulting displacement of the medium at any location is the sum of the displacements of the individual waves at that same location.
When waves have the same amplitude and same frequency then at a particular point it can be:
Constructive Interference - When both waves have displacement in the same direction (In phase) and thus there vectors get added to form an even larger displacement.
Constructive Interference - When both waves have displacement in the same direction (In phase) and thus there vectors get added to form an even larger displacement.
Destructive Interference - This occurs when the waves have different direction of displacement (1 up, 1 down; Out of phase; difference 180 degrees) and thus they cancel each other creating a smaller displacement to one direction or none at all.
Square waves
Square waves are non-sinusoidal waves like the previous ones. These waves change
their amplitude abruptly and oscillate between fixed values. The graph above
shows the nature of Square Waves that consist solely of vertical and horizontal
lines.
The waves vary between fixed minimum and maximum points at a steady frequency.
In the above ideal Square wave the transition between Maximum and Minimum as we can see on the points x= 1; 2; 3; 4 are
instantaneous.
These waves are often found in electronics and signal waves. Square waves are always encountered in digital switching circuits and are
produced by the binary logic devices.
In sound terms these waves are said to sound hollow.
their amplitude abruptly and oscillate between fixed values. The graph above
shows the nature of Square Waves that consist solely of vertical and horizontal
lines.
The waves vary between fixed minimum and maximum points at a steady frequency.
In the above ideal Square wave the transition between Maximum and Minimum as we can see on the points x= 1; 2; 3; 4 are
instantaneous.
These waves are often found in electronics and signal waves. Square waves are always encountered in digital switching circuits and are
produced by the binary logic devices.
In sound terms these waves are said to sound hollow.