ELFT 533 – Broadcast Engineering and Applied Acoustics
Acoustics
Sound
· is the wave motion consisting of series of compressions and rarefactions produced in the transmitting medium by a vibrating body.
· a longitudinal wave which propagates through a medium and able to cause the sensation of hearing.
Requirements to Produce Sound
· pressure of a vibrating body
· presence of transmission medium (elastic)
Interpretation of Sound
1. Objectively
sound is a physical phenomenon consisting of wave motion in air or other sound transmitting medium.
2. Subjectively
sound is a sensation produced by outside stimulation and occurring in the organ of hearing.
Properties of Sound
1. Frequency (f)
number of vibrations per unit time.
2. Period (T)
time to complete one resolution.
3. Wavelength
length of one complete wave or cycle.
4. Velocity of propagation
depends on the nature of the medium
For solids:
Y = Young's Modulus of Elasticity (dyne/cm2)
d = density of solid (g/cm3)
For liquids:
B = Bulk's Modulus of Elasticity (1/compressibility)
d = density of the liquid
For gases:
k = specific heat constant
p = pressure
d = density
for air at 0ºC
for air at 20ºC
k = 1.405
p = 1.008 x 106 dynes/cm2
d = 0.001205 gm/cm2
Velocity of Sound in air at any temperature (T) and normal pressure
5. Intensity of Sound
the intensity of sound is the time rate at which the sound energy flows through a unit area normal to the direction of propagation
For an Isotropic Source:
Intensity Level of Sound (dB)
Example: A small source of sound radiates acoustic energy uniformly in all directions at a rate of 1.5 W. Find the intensity and the intensity level at a point 25 meters from the source if: a) there is no absorption and b) there is 10 % absorption in the 25-meter path.
The decibel Notation System
Definition of bel:
Common dB Notations and Standard References
Quantity / Standard References / Symbol / Log MultiplierSound Pressure Level / 1 dyne/cm2 (H2O)
0.0002 dyne/cm2 (Air)
0.00002 N/m2 / dBSPL / 20
Sound Intensity Level / 10-16 W/cm2 / dBRAP / 10
Sound Power Level / 10-12 W/m2 / dBPWL / 10
Audio Power / 10-3 W / dBm / 10
Volume Unit / 10-3 W / dBVU / 10
Voltage / 1 V / dBV / 20
Current / 1 mA / dBA / 20
In general,
Combining Decibels
Examples:
1. Find the power in watts:
a. 30dBm
b. -12dBm
c. 13dBP
2. The total sound intensity level is dependent on the sum of all individual sound energy intensity existing at the same time measurement. If two pure tones of different frequencies are produced simultaneously with one tone having an intensity level of 80 dBRAP and the other having 81.5 dBRAP. What is the resultant intensity level?
3. Consider block X as an amplifier that provides gain X dB if: a) PIN = 10 dBm and POUT = 100 dBm, determine X; b) X = 10 dBm and PIN = 10 dBm, determine POUT; c) if PIN = 13.0103 dBW + 43.0103 dBm and X = 5 dB, determine POUT.
Threshold of Audibility
- the minimum effective sound pressure of a signal that is capable of evoking an auditory sensation
Threshold of Tolerance or Field of Audition
- range of sound pressure which the human ear can withstand without discomfort or pain and evoke an auditory sensation
Threshold of Pain or Feeling
- maximum sound pressure which the human ear withstand without discomfort or pain
Physiological Characteristics of Sound
1. Pitch
- frequency vibration of pure tone
- determines the highness or lowness of note or tone
2. Timbre
- quality of sound
- depends on the mode of vibration
3. Loudness
- describes the strength of auditory sensation produced by a sound
- depends on intensity or the amplitude of vibration or energy
Loudness Level
- measured by the SPL of a standard pure tone of specified frequency which is assessed by normal observers as being equally loud
Classification of Sound According to Form and Frequency of Vibration
1. Noise
- irregular vibration which does not have a definite range of frequency
2. Music
- regular in vibration
- consists of fundamental frequency and harmonics whose combination is pleasing to the ear
Transmission of Sound
Three possibilities that may happen to sound:
1. Reflection
- return of a wave from the boundary of the medium
2. Absorption
- energy is transformed into something else, generally heat energy
3. Onward Transmission
- if there is a change in medium, the magnitude of sound will also be changed
Acoustical Phenomena due to Reflection
1. Echo
- repetition of sound wave produced by the reflection of sound as it strikes an obstruction
2. Flutter
- uneven decay of sound that causes a tiresome hearing sensation
3. Interference
- uneven sound intensity due to reinforcement and cancellation of sound waves
4. Reverberation
- persistence of sound on an enclosure as the result of continuous reflection of sounds at the wall after the sound source has been turned off
Room Acoustics
It is concerned with the behavior of sound within an enclosed space with a view to obtain the optimum effect on the occupants.
Reverberation Time (RT60)
- defined as the time required for sound energy in the room to drop to one-millionth of its initial value, equivalent to the relative intensity dropping by 60dB
- varies with room size, use and acoustical properties of the material
- depends on room volume, the total surface area and the total absorption in the room
Optimum Reverberation Time
– when the reverberation is just right.
– depends on:
a. volume of room
b. use of the room
Two Types of Acoustic Room
1. Dead Room
2. Live Room
Essential Parameters of a Room
1. Internal volume
2. Total internal reflecting area of the surface
3. Absorption coefficient of different surfaces (a)
Reverberation Time Equations
1. Sabine’s Equation
- applicable for medium to large-sized rooms with RT60 ³ 2 seconds
where:
2. Norris – Eyring Equation
- applicable for rooms with RT60 £ 2 secconds
3. Stephens and Bate Equation
Absorption Coefficient of Materials ( per ft2)
open window 1
brick wall 0.02
tile 0.03
concrete 0.02
glass 0.03
curtain 0.5
plaster 0.03
wood 0.05
people 4.7
Examples:
1. A classroom 60 ft long by 35 ft wide by 15 ft high has sound absorption coefficient of 0.03 for wall, 0.04 for ceilings and 0.10 for floors. Find the RT60 in this space with no occupants and no sound absorbing treatment.
2. A classroom has a volume of 400 ft3. There are exposed 600ft2 of tile and 500 ft2of woods in chairs, doors and woodwork. There are 30 people in the room. Estimate the RT.
3. A shower room has the dimension 5 x 4 x 3. All walls are tile and the door has an absorption coefficient as tile. Find the RT.
4. A lecture room, 16 m long, 12.5m wide and 5 m high has a reverberation time of 0.75 seconds. Calculate the average absorption coefficient of the surfaces using the Eyring Formula.
5. An auditorium has plaster walls and ceiling, a wooden floor, and 500 seats. What is the reverberation time when empty? When seats are filled? The auditorium is 100 ft long, 50 ft wide and 30 ft tall.
- 6 –
ermtiong