CSD 637 - Instrumentation Formulas

Formulas for Quiz 1

Frequency (f)

cycles/second (Hz)
1/T

Period (T)

 time for one cycle (s or ms)

1/f

Wavelength (λ)

distance per cycle
v / f (v ≈ 340 m/s)

Period = ? , Wavelength = ? , both describe ? cycle

period = time

wavelength = distance

both describe ONE cycle

Sine wave features

peak, peak-to-peak, zero crossings, period

RMS amplitude

 0.707 × peak (for sine waves)

RMS relates to perceived ___

energy

 peak-to-peak is __× peak.

2

Speed of sound in air (v)

~340 m/s

The period of 1000 Hz = __ ms

1

1 ms = ___ s

0.001 s

1 µs = ?

1 × 10⁻⁶ s

Hearing is ___

nonlinear

Frequency and intensity are perceived on ___, not linear

log scales

Audiogram uses ___ frequency spacing and dB scales

octave

Range of human hearing

 ~20 Hz – 20 kHz

Basilar membrane = ?

frequency analyzer

Loudness perception is ___ (equal loudness contours).

nonlinear

Linear → ___ a constant.

add

Log → ___ by a constant.

multiply

Absolute → fixed reference. Units?

Pa, W/m²

Relative → compared to __

reference (dB)

Octave =__ or __ frequency.

2× or ½

Decade = _ or _ frequency.

10× or 1/10×

what are Decibels (dB)

Relative units based on ratios of the absolute units relative to a reference

dB IL formula

10 log₁₀ (I / 10⁻¹² W/m²)

dB SPL formula

20 log₁₀ (p / 20 µPa)

Reference intensity

 1 × 10⁻¹² W/m² → 0 dB IL

Reference pressure

20 µPa = (20 × 10^-6 Pa) → 0 dB SPL

Doubling pressure → __ dB

+6

Doubling intensity → __ dB

+3

Halving = __ dB (intensity) or _ dB (pressure).

-3, -6

1 dB IL = __ dB SPL (IL and SPL are interchangeable as relative measures).

1

Intensity is proportional to pressure ___

squared

formula for intensity of a sound wave

I = p²/pc

in the formula for intensity of a sound wave (I = p²/pc), what does “I” mean?

sound intensity (W/m²)

in the formula for intensity of a sound wave (I = p²/pc), what does “p²” mean?

sound pressure (Pa)

in the formula for intensity of a sound wave (I = p²/pc), what does “p” mean?

density of the medium (kg/m³)

in the formula for intensity of a sound wave (I = p²/pc), what does “c” mean?

speed of sound in the medium (m/s)

formula for work

force x distance

formula for Joules

J = Nm

formula for pressure

force/area

2 μPa __

peak

4 μPa __

peak-to-peak

Peak value formula

RMS/.707

10× intensity = ?

 +10 dB

10× pressure = ?

+20 dB

Doubling distance = ?

–6 dB

Adding equal uncorrelated sources → ?

+3 dB

MOST of the time sounds are uncorrelated with each other - ___ in phase!

NOT

The distance between compression cycles in an ongoing pure tone is the same as the wavelength of the tone.

true

how to do inverse log on the calculator

SHIFT → log → number you’re calculating

Which of the following is a vector quantity in the context of sound?

Particle velocity

formula for dB

10logx
x= # you’re given