**Table Of Contents**

** General Wave Characteristics **

direction of particle oscillation is perpendicular to the__Transverse Wave:__**propagation**of the wave. Think above moving a string with a fixed point by moving the hand up and down.- Includes electromagnetic waves like visible light, microwaves, and x-rays.
- In any waveform, energy is delivered in the direction of wave travel

particles of wave oscillate parallel to the direction of transfer__Longitudinal Waves:__- Sound waves, causes air particles to oscillate through cycles of
**compression**and**rarefaction (decompression)**along the direction of the wave.

- Sound waves, causes air particles to oscillate through cycles of

** Describing Waves **

Distance from one maximum (__Wavelength:__**Crest)**to another crest or valley to valley.Number of wavelengths passing a fixed point per second [Hz].__Frequency:____Propagation Speed:__*v = fλ*The inverse of frequency and is defined as the number of seconds per cycle.__Period:____Angular Frequency:__*w = 2πf = (2π)/T*Waves oscillate about this center point.__Equilibrium Position:__**Displacement**is how far a particular point on the wave is from the equilibrium position. Maximum magnitude is called the**Amplitude**.

** Phase **

- Can calculate a
**phase difference**to compare two waves passing through the same phase. - If completely out of phase, expressed as a difference of λ/2 or 180 degrees.

** Principle of Superposition **

- When waves interact with each other, the displacement of the resultant wave at any point is the sum of the displacements of the two interacting waves.
If waves are in-phase, the displacements always add together. Resultant amplitude will be 2x the original amplitudes.__Constructive Interference:__Two out of phase waves cancelling each other out completely.__Destructive Interference:__

** Travelling and Standing Waves **

**Travelling Waves:**are when the waves are moving and can be modelled as a string with one free end and one fixed end.Only apparent movement of string is fluctuation of amplitude at fixed points along the length of the string. Can be modelled by a string with two fixed end or an open ended pipe__Standing Waves:__Where amplitude is constantly zero__Node:__At midway point between nodes, fluctuate at maximum amplitudes.__Antinode:__

** Resonance **

- Every object has a
**natural (resonant) frequency**when struck and allowed to vibrate freely. The quality of sound is determined by the natural frequency.__Timbre:__- Objects that produce multiple non-harmonious or unrelated frequencies produce
**noise**. - Musical sounds are usually objects that vibrate with multiple natural frequencies which are whole-number multiples of the fundamental frequency (
**fundamental pitch & overtones**).- Can usually hear about 20-20000 Hz for healthy adult, high frequency hearing declines with age.

- If frequency of forced oscillated is close to or equal to natural frequency, amplitude of wave becomes exponentially higher (
**Resonating**).- Amplitude would go to infinity without the presence of
**damping**, which is caused by frictional forces. : The decrease in amplitude of a wave caused by a non-conservative force.__Damping__

- Amplitude would go to infinity without the presence of

** Sound **

A longitudinal wave transmitted by the oscillation of particles in a deformable medium. Cannot travel through a vacuum. Speed of sound is given by:

- v = √(B/ρ)
- B is the bulk modulus (increases from gas to solid)

** Production of Sound **

- The mechanical distribution of particles in a material along the sound wave’s direction of propagation. Particles vibrate along an equilibrium position which causes area of compression and decompression.
- Particles themselves do not move, but alternating areas allows for propagation of wave.

** Frequency and Pitch **

**Pitch**is the same thing as frequency. A lower pitch indicates a lower frequency. We just perceive pitch while frequency is more mathematics.- Soundwaves below 20 Hz are called
**infrasonic**& soundwaves above 20,000 Hz are called**ultrasonic waves.**

** Doppler Effect **

- Describes the differences between the actual frequency of a sound and the perceived frequency of a sound.
- If the source and the detector are moving towards each other, then the frequency is perceived to be higher. Vice Versa for if they’re moving away from each other.
- f’ = f (v ±
*v*)/(v ±_{D}*v*)_{s } *v*is the speed of sound in the medium,*v*is the speed of the detector, and_{D}*v*is the speed of the source._{s}- Upper sign used when the source moving towards, lower signs used when the source is moving away.

- f’ = f (v ±

- If the source and the detector are moving towards each other, then the frequency is perceived to be higher. Vice Versa for if they’re moving away from each other.
- Can be visualized as sound waves in front of a moving object as being compressed, while the sound waves behind the object are stretched out

** Shock Waves **

- If an object is producing sound and moving at a speed above the speed of sound, then wave fronts begin to build upon one another at the front of the object.
The highly condensed wave which creates a high pressure, followed by a low pressure (__Shock Wave:__**sonic boom)**.

** Intensity and Loudness of Sound **

- Loudness is the way humans perceive the intensity of a sound.
the average rate of energy transfer per area across a surface that Is perpendicular to the wave. (Power transported per unit area)__Intensity:__- I = P/A, P is the power & A is the Area

- Intensity is proportional to the square of amplitude.
- Intensity is inversely proportional to the square of the distance from the source.
is measured in__Sound Level__**decibels (dB)**: β = 10 log (I/Io)*I*is the threshold of hearing which is 1 x 10_{0}^{-12}W/m^{2 }- If intensity is changed by some factor, can use: βf = βi + 10 log (If/Ii)

** Attenuation **

- Real world measurements of sound will be lower than those expected from calculations. Which is a direct result of
**damping/attenuation**. - Since sound is simply oscillations in simple linear motion, they are subject to non-conservative forces which cause a decrease in amplitude as the oscillation progresses.
- Pitch does not change because of damping.

** Beat Frequency **

- When two sounds of slightly different frequencies are produced in proximity:
- fbeat = f1 – f2

** Standing Waves **

- Occur when two waves of the same frequency are travelling in different directions and interfere with each other.
- As waves move in opposite directions, they interfere to produce new wave patterns characterized by alternating points of maximum amplitude (Antinode) & points of no displacement (node).
- Objects that support standing waves have boundaries at both ends
do not allow oscillation and correspond to nodes.__Closed Boundaries:__Allow maximum oscillation and correspond to antinodes.__Open Boundaries:__

** Strings **

- λ = (2L)/n
*n*is an integer number called the**harmonic**, which corresponds to how many half-wavelengths are supported by the string. Equal to number of antinodes.

- f = (nv)/(2L)
- The
**fundamental frequency**is the lowest frequency of a standing wave. At n=2, the frequency is known as the first overtone or the second harmonic.- First overtone has half the wavelength and twice the frequency of the first harmonic.

- The
- All possible frequencies that can be supported are known as the
**harmonic series.**

** Open Pipes **

- Open pipes are open at both ends, while closed pipes have one end closed.
- These are basically the exact opposite of strings. The number of nodes, between the antinodes on each end, corresponds to what harmonic frequency the pipe is in.
- Same equations as above are used.

** Closed Pipes **

- A node on the closed end and an antinode on the open end. First harmonic is when there are only these two initial points. Corresponds to one quarter of a wavelength.
- Each harmonic is equal to the number of
**quarter-wavelengths**supported by the pipe. (half-wavelengths in open pipes and strings)

- Each harmonic is equal to the number of
- There can only be odd numbered harmonics since an even number would require synonymous pipe ends.
- λ = (4L)/n
- f = (nv)/(4L)
- n can only be odd number interger.

** Ultrasound **

- Use high frequency sound waves outside the range of human hearing to compare the relative densities of tissues in the body.
- The transmitter produces a pressure gradient and acts as a receiver which processes the reflected sound.
- Ultimately relies on the reflection of the wave.
used to determine flow of blood within body by measuring the frequency shift that is associated with movement towards or away from the receiver.__Doppler Ultrasound:__