Auditory Theory: Acoustics

Lecture 002 Sound I

• Length ÷ Time = Velocity (meters per sec or ms^-1)
• Velocity ÷ Time = Acceleration (meters per sec per sec or ms^-2)
• Acceleration x Mass = Force (newtons)
• Force ÷ Area = Pressure (kg in^-2)
• Force x Distance = work (joules or ftlbs )
• Work ÷ Time = Power (watts)

• = square root
• A = area
• ν (nu) = the speed in metres per second (ms^-1)
• ρ (rho)= the density of the material (in kgm^-3) and
• Ε = the Young's modulus of the material (in Nm^-2)
• P = the pressure of the gas (in Nm^-2)
• V = the volume of the gas (in m³) and
• γ (gamma)= is a constant which depends on the gas (1.4 for air)
• m = the mass of the gas (in kg)
• M = the molecular mass of the gas (in kg mole^-1)
• N = force in Newtons
• R = the gas constant (8.31 J Kg mole^-1) and
• T = the absolute temperature (in Celsius)
• μ (mu) = the mass per unit length (in kg m^-1) and
• T = the tension of the string (in N)
• π (pi)= PI (3.142) the ratio of the radius to the circumference
• r = the radius
• W = Watts
• I = intensity
• J = Joule measure of energy
• λ (lambda) = wavelength
• f = frequency
• f₀ = fundamental
• f_n = harmonic n

Scientific Notation

The exponent system is a common method for dealing with large numbers and you should take the time to understand it.

Exponents are arrived at by dividing the large number by tens (or any base you choose) and then expressing the result as a N * 10^x. One shortcut is that the exponent always indicates the number of zeros that appear after the 1.

Negative Exponents

In the equations that follow and throughout this course you will encounter negative exponents which may be a new concept for you. They are simply a shorthand for the reciprocal (1/x)

So

• 10² = 100
• 10^-2 = 1/100 = 0.01
• ms²= meters x seconds ²
• ms^-1 = meters x (1/seconds) = meters per second
• ms^-2= meters x ((1/(seconds) / seconds) = meters /second/second