Auditory Theory Math Calculators
Index
US to Metric Conversions
Metric to US Conversions
Exponents
Speed of sound in materials
Speed of Sound in Air
Wavelength, Frequency and Velocity
Pressure, Velocity and Impedence
Logarithms
Sound Intensity Level
(SIL)
Sound Power Level
(SWL)
Sound Pressure Level
(SPL)
Add Decibels
Adding equal uncorrellated sounds
Intensity as a function of distance
The effect of boundaries
Refraction
Interference at speakers
Standing wave between two boundaries
Standing wave harmonics
Standing wave in mixed boundaries
Calculating 16 harmonics
Index
Decimal to 10 base
Decimal:
Number:
x 10^
And in reverse
10 base to Decimal
10(base) to the power of (exponent)
Number:
Base:
Exponent:
Decimal:
Index
Speed of sound in solids
Velocity (v)= sqrt(Young'sModulus(E)/Density(d))
Young's Modulus
Young's Modulus Base:
Young's Modulus Exponent:
Density:
kg/m^3
Velocity:
m/sec
Material
Young's Modulus (N/m2)
Density (kg/m3)
Speed of sound m/sec
Steel
2.10 x 10^11
7800
5,189
Aluminum
6.90 x 10^10
2720
5,037
Lead
1.70 x 10^10
11400
1,221
Glass
6.00 x 10^10
2400
5,000
Concrete
3.00 x 10^10
2400
3,536
Water
2.30 x 10^9
1000
1,517
Air (at 20C)
1.43 x 10^5
1.21
344
Beech wood(along the grain)
1.40 x 10^10
680
4537
Beech wood(across the grain)
8.80 x 10^10
680
1138
Index
Speed of Sound in Air
velocity = 20.1 x sqrt(273+ temp in Celsius)
Temperature:
Celsius
Velocity :
m/sec
Meters to travel:
m
Time taken:
milliseconds
Index
Wavelength, Frequency and Velocity
velocity(v) = frequency(f)*wavelength(lambda)
Frequency:
Hz
Wavelength:
m
Velocity
:
m/sec
frequency(f) = velocity(v)/wavelength(lambda)
Velocity
m/sec (for air)
Wavelength
m
Frequency:
Hz
wavelength(lambda)= velocity(v)/frequency(f)
Velocity
m/sec (for air)
Frequency:
Hz
Wavelength:
m
Index
Pressure, Velocity and Impedence
Impedence(Zacoustic) = sqrt(pressure amplitude(p)*Youngs Modulus(E))
Pressure:
kg/m^2
Young's Modulus :
Young's Modulus Base :
Young's Modulus Exponent:
Impedence:
kg/m^2/sec
Index
Logarithms
Input decimal number >0=
Logarithm=
Index
Sound Intensity Level
SIL = 10 log10(I actual/ I reference)
Emitter Diameter=
cm
Radiated Power=
milliWatt
Sound Intensity =
W/m^2
I reference =
1/10^12 Watts /m^2 (1 pico watt)
Sound Intensity Level =
dB
Index
Sound Power Level
SWL = 10 log10(Watts actual/ Watts reference)
Actual Power
Watts
I reference =
1/10^12 Watts /m^2 (1 pico watt)
Sound Power Level =
dB
Index
Sound Pressure Level (SPL)
SPL = 20 log10(Actual Pressure/ Reference Pressure)
Actual Pressure
Pascal
I reference =
1/10^6 Pascal /m^2 (1 micro Pascal)
Sound Pressure Level =
dB
Index
Adding Decibels
SPL = 20 log10(sqrt(P1^2+p2^2+PN^N)/P reference)
Sound 1 Level:
dB
Sound 2 Level:
dB
Summed SPL:
dB
Index
Adding equal uncorrelated sounds
P total = P1+(3*N)
Sound level of one source:
dB
Number of Sources:
Total level:
dB
Index
Intensity as a function of Distance
SIL = 10 log10(Watts source/Watts reference)-20 log10(radius) - 11db
Sound source intensity:
Watts
Distance from source
meters
Distant SIL:
dB
Index
The effect of boundaries
SIL = 10* log10(W actual/W reference) +10 * log10(Q) -10 * log10(4*PI ) - 20* log10 (radius)
Power of source:
Watts
Distance from Source:
meters
Q:
Sound Intensity at distance:
dB
Index
Change in Angle due to Refraction
Sine Theta 1/Sine Theta 2 = sqrt(Temperature1/Temperature2)
Temperature of Layer 1
Celsius
Temperature of Layer 2
Celsius
Angle of refraction:
Index
What freqencies will cancel for a listener on axis to one speaker?
Distance between speakers:
meters
Distance to listener:
meters
frequency of wavelength/2:
frequency of wavelength/3:
Index
Standing wave between two boundaries
frequency (f) lowest = Velocity of sound (v)/2*distance between boundaries (L)
Distance between boundaries:
meters
Speed of sound:
meters/sec
Lowest Standing Wave:
Hz
Index
Standing wave harmonics
frequency (f) lowest = (N*Velocity of sound v)/(2*distance between boundaries L)
Distance between boundaries:
meters
Speed of sound:
meters/sec
Harmonic Number:
Lowest Standing Wave:
Hz
Index
Standing wave in mixed boundaries
frequency (f) lowest = ((2N+1)*Velocity of sound v)/(4*distance between boundaries L)
Distance between boundaries(L):
meters
Speed of sound(V):
meters/sec
Harmonic Number(N):
Lowest Standing Wave:
Hz
Index
Calculating 16 harmonics
Fundamental:
Hz
Second Harmonic:
Hz
Third Harmonic:
Hz
Fourth Harmonic:
Hz
Fifth Harmonic:
Hz
Sixth Harmonic:
Hz
Seventh Harmonic:
Hz
Eighth Harmonic:
Hz
Ninth Harmonic:
Hz
Tenth Harmonic:
Hz
Eleventh Harmonic:
Hz
Twelfth Harmonic:
Hz
Thirteenth Harmonic:
Hz
Fourteenth Harmonic:
Hz
Fifteenth Harmonic:
Hz
Sixteenth Harmonic:
Hz