AOpen AX4L-N Uživatelský manuál

Resonance in acoustic tubes1. wavelength2. plain wave propagation3. reflection4. phase matching

Sound traveling in a closed tube reflects off the ends of the tube.

Sound traveling in an open tube also reflects off the ends of the tube.Reflection off of a soft surface

The vocal tract is a tube that is openat one end and closed at the other.has two kinds of reflection:1. hard surface at closed end2. soft surface a

Sound waves traveling though spaceinterfere with each other.ABdirectiondirection

Destructive interference: A + B = 0ABdirectiondirectionA+B

Constructive interference: A + B = ABABdirectiondirectionA+B

Constructive interference: A + B = ABABdirectiondirectionA+B112

Constructive interference: A + B = ABABdirectiondirectionA+B-1-1-2

Reflected waves in a tube interfere with each other.constructive interference = resonancedestructive interference = nonresonance

Q: What frequencies will resonate in a tube?= Q: What sine waves will show constructive interference?two factors - wavelength and tube lengthkey: w

Two ways to measure the period of a sine wave.Time Frequency = 1 / Time

An example of reflecting “in phase”- a sine wave that “fits” in a closed tubewavelength = tube length

An example of reflecting “in phase”- a sine wave that “fits” in a closed tubewavelength = tube lengththe reflectedwave is in phaseΔ constructive in

An example of reflecting “in phase”- a sine wave that “fits” in a closed tubewavelength = tube lengththe reflectedwave is in phaseΔ constructive in

Another example of reflecting “in phase”- a sine wave that “fits” in a closed tubewavelength = ½ * tube length

A general formula for calculating the resonant frequencies of sine waves that will resonate in a tube closed at both ends:Fn = nc/2Ln = resonant fr

Now consider a tube that is open at one end, and closed at the other.

Now consider a tube that is open at one end, and closed at the other.Reflection from the open end is different.Phase shift!

A sine wave that “fits” in a tube that is open at one end, and closed at the other.

phase shift atopen endA sine wave that “fits” in a tube that is open at one end, and closed at the other.

A sine wave that “fits” in a tube that is open at one end, and closed at the other.phase shift atopen endλ

Sound: pressure fluctuation that travels through space.Speed of sound = 35,000 cm/sSpaceWavelength = spatial period

A sine wave that “fits” in a tube that is open at one end, and closed at the other.phase shift atopen endλresonant frequency is: f = c/(4/5*L)

Another sine wave that “fits” this tube.

λresonant frequency: f = c/(4/3L)

A general formula for resonant frequenciesof tubes open at one end and closed at the other:fn = (2n-1)c/4Ln = resonance number (1,2,3...)c = speed

the vowel schwa [ә]:a tube open at one end (lips) and closed at the other (glottis)Vocal tract length: ~ 17.5 cmF1 = c/4L = 35,000/70 = 500 HzF2 =

Peter Ladefoged saying [ ә ]:2500 Hz1250 Hz 400 Hz

Wavelength = speed of sound * period durationλ = c * Tλ = c / f because f = 1 / TSpaceWavelength = spatial period

1. wavelength. Sine wave has a spatial period, peaks and valleys located in space.Space

sound propagates from source in a sphere.

However, sound in a tube propagates in a plane – effectively, no curvature

However, sound in a tube propagates in a plane – effectively, no curvature2. Plane wave propagation

3. ReflectionSound reflects off of surfaces - more reflection off of hard surfaces - less reflection off of soft surfaces - scattered reflection of