Acoustics

• 1. Sound Source
• 2. Transmitting Medium
• 3. Receiving Mechanism

• Mass (inertia)
• Stiffness (elasticity)

• Wavelength is the distance (in m) between successive areas of condensation (or rarefaction)
• Wavelength is dependent on frequency of vibration and speed of sound
• Wavelenth is inversly proportional to the frequency of vibration
• λ = speed of sound (meters per second)/frequency (Hz)

• Sound Pressure- Force per unit area. Pascal = N/m2
• Sound Intensity- Rate of energy flow per unit area; the rate at which energy is transferred by a unit area. W/m2

• If the energy radiated by the source is constant and if the source provides a spherical wave, then the intensity of the sound wave deminshes as it moves from the source. Specifically, intensity decreases as the inverse square of the distance from the source.
• I OC 1/r(squared)
• Example:What is the sound intensity at 6 m relative to 3 m? In other words, what is the decrease in intensity if you double the distance from the source?
• I OC 1/r(squared)
• You have doubled the distance. Therefore, r = 2
• I OC 1/2(squared) = I OC 1/4
• Sound pressure is iversely related to distance. Pressure decreases as the inverse of the distance from the source
• I OC p(squared) OR p OC √ I
• p OC 1/r
• Example 1:What is the sound pressure at 6 m relative to 3 m? In other words, what is the decrease in pressure if you double the distance from the source?
• p OC 1/r
• You have doubled the distance. Therefore, r = 2.
• p OC 1/2
• If you double the distance from the source, you will have 1/2 the sound pressure.

• Transmission- movement or propagation of a sound wave through a medium
• Reflection- If a sound wave being transmitted through a medium encounters an obstacle (e.g. a change in the medium), a portion of the sound wave will be reflected back from that obstacle
• Absorption- Acoustic energy that is dissipated or lost in the form of heat. Will occur when a sound wave encounters a source of friction.
• Diffraction- Property by which sound "bends" or passes around objects with dimensions smaller than the wavelength of the sound wave. A soundwave can be affected by obstacles in its pathway. If the dimensions of the object are smaller than the wavelength of the sound wave, sound diffraction will occur. Low-frequency phenomenon.

Property by which sound intensity is decreased on the far side of an obstacle. When a sound wave encouners an obstacle that is = or > its wavelength, sound diffraction (bending) will NOT occur. Rather, the object "casts a shadow." There will be an area on the far side of the obstacle where the sound intensity has been reduced. High frequency phenomenon.

• An air-filled cavity can be thought of as having elements of mass, stiffness, and resistance (friction)
• Impedance due to mass is dependent on frequency. The mass opposses high-frequency motion. If mass is increased, there is greater opposition to the flow of high-frequency energy. Directly proportional to the neck of the tube(l). Inversely proportional to the diameter of the neck
• Acoustic compliance is proportional to the volume of the rigid-walled cavity.
• Stiffness is related to the compressibility of air within the air-filled rigid-walled cavity. Inversely proportional to the volume of the rigid-walled cavity.
• fr = 1/√ MC
• where M = Mass and C = Compliance

• The air in the tube will have maximum amplitude of vibration when the applied frequency has a wavelength 2times the length of the tube AND at integer multiples of that frequency.
• f(most difficult to figure out)
• 2f
• 3f etcetera
• Length of the tube = 1/2 of the wavelength
• Example:Tube of 1 meter.The tube resonates best when the applied frequency has a wavelength 2 times the length of the tube.THUS, λ = 2 meters
• λ = 343 m/s / frequency (Hz)
• f = 343 m/s / λ
• f = 343 m/s / 2
• f = 171.5 Hz (best frequency)
• There also are resonances at 2f, 3f, etcetera.
• 2f = 343 Hz
• 3f = 514.5 Hz
• Etcetera.

• The air in the tube will have maximum amplitude of vibration when the applied frequency has a walength 4times the length of the tube AND at odd integer multiples of that frequency.
• f
• 3f
• 5f
• Lenth of the tube = 1/4 of the wavelength
• Example:Tube of 1 meter.The tube resonates best when the applied frequency has a wavelength 4 times the length of the tube.THUS, λ = 4 meters
• λ = 343 m/s / frequency (Hz)
• f = 343 m/s / λ
• f = 343 m/s / 4
• f = 85.75 Hz (best frequency)
• There also are resonances at 3f, 5f, etcetera.
• 3f = 257.25 Hz
• 5f = 423.75 Hz
• Etcetera.

• Mass per unit volume. If there are more particles per unit volume or more mass per partice, then the substances will be more dense
• kg/m(cubed)

When air particles near a certain point in space are closer together than normal (equlibrium), a state of condensation exists. The air molecules adjacent to the vibrating object are compressed to create an area with greater density. Consequently, there is an area of increased pressure.

When air particles near a certain point in space are further apart (i.e., “spread out”) than normal (i.e., equilibrium), a state of rarefaction exists. The density of the air molecules is decreased. Consequently, there is an area of decreased pressure.

• ( λ ) (Unit = meter, m): The distance (in meters) between successive areas of condensation (or rarefaction).Wavelength is dependent on two factors:
• 1. Frequency of vibration
• 2. Speed of sound.

The movement (propagation) of a disturbance through a medium such as air without permanent displacement of the particles themselves

Composed of layers of condensation and rarefaction radiating in all direction

When the areas of condensation (or rarefaction) of 2 sound waves of equal frequency overlap (in phase)

When the area of condensation of one sound wave overlaps with the area of rarefaction of another sound wave. (180(degress) out-of-phase)

A soundfield without obstacles. Sound transmission occurs without interfernce (sound diffraction, absorption, reflection)

Prolongation of sound. When sound is generated in an environment, there is a process of multiple reflections that takes place from surrounding obstacles or sufaces that results in the prolongation of sound

Vibratory responce to an applied force

"Something" set into vibration by the action of another vibration of force

• An air filled cavity that can be set into vibration by the action of another vibration or force. Enclosed volumes of air can be set into vibration
• 2 basic types
• Helmholtz
• Tube Resonator

When sound is generated within an enclosure, some of the sound impinging upon the surfaces will be reflected. All points in the enclosure are acted upon by 2 sound waves. A stationary pattern of sound wave interaction is known as a standing wave. Standing waves are generated by a fixed pattern of constructive and destructive interference.