Auditory Theory Math Calculators

Index
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