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17 results for “acoustics”

Formulae (17)

Equal-Temperament Note Frequency

f_n = f_0 \times 2^{n/12}

Frequency of a note n semitones from a reference pitch.

Music & AcousticsBasic

Octave Frequency Ratio

f_2 = 2 f_1

An octave above a note has exactly double its frequency.

Music & AcousticsIntermediate

Sound Intensity Level (dB)

L = 10 \log_{10}\!\left(\frac{I}{I_0}\right)

Sound intensity expressed in decibels relative to the hearing threshold.

Music & AcousticsAdvanced

Combining Two Sound Levels

L = 10 \log_{10}(10^{L_1/10} + 10^{L_2/10})

Total level when two sound sources play together.

Music & AcousticsBasic

Wave Speed

v = f \lambda

Sound speed equals frequency times wavelength.

Music & AcousticsAdvanced

Vibrating String Frequency

f = \frac{1}{2L}\sqrt{\frac{T}{\mu}}

Fundamental pitch of a string from length, tension and mass.

Music & AcousticsIntermediate

Harmonic Series

f_n = n f_1

Overtones of a note are whole-number multiples of the fundamental.

Music & AcousticsAdvanced

Pitch Interval in Cents

c = 1200 \log_2\!\left(\frac{f_2}{f_1}\right)

Measures the size of a musical interval in cents.

Music & AcousticsBasic

Beat Duration from Tempo

t = \frac{60}{BPM}

Length of one beat in seconds from the tempo.

Music & AcousticsIntermediate

Delay Time for Tempo

t_{ms} = \frac{60000}{BPM}

Milliseconds per beat, used to sync echo/delay effects to a song.

Music & AcousticsAdvanced

Doppler Pitch Shift

f' = f\,\frac{v + v_o}{v - v_s}

Observed pitch changes as a source moves toward or away.

Music & AcousticsAdvanced

Room Resonance (Axial Mode)

f = \frac{c}{2L}

Lowest standing-wave frequency between two parallel walls.

Music & AcousticsBasic

Frequency and Period

f = \frac{1}{T}

Frequency is the reciprocal of the wave's period.

Music & AcousticsIntermediate

Open Pipe Fundamental

f = \frac{v}{2L}

Lowest note of a pipe open at both ends (like a flute).

Music & AcousticsBasic

Perceived Loudness Doubling

\Delta L = 10\,\text{dB}

A 10 dB increase is heard as roughly twice as loud.

Music & AcousticsAdvanced

Sabine Reverberation Time

RT_{60} = 0.161\frac{V}{A}

Time for sound to decay 60 dB in a room.

Music & AcousticsAdvanced

Mel Scale (Pitch Perception)

m = 2595 \log_{10}\!\left(1 + \frac{f}{700}\right)

Converts frequency to the perceptual mel pitch scale.