Resonant Waves in A Vibrating Column of Air For a tube open at both ends:

Resonant Waves in A Vibrating Column of AirFor a tube open at both ends:

Resonant Waves in A Vibrating Column of Air

When air is blown across one end, the pressure disturbance moves through the tube to the other end, and a resonance is set up:

For a tube open at both ends:

Resonant Waves in A Vibrating Column of Air

When air is blown across one end, the pressure disturbance moves through the tube to the other end, and a resonance is set up:

For a tube open at both ends:

Low pressureLow pressureHigh pressure

Resonant Waves in A Vibrating Column of Air

Max Particle Displacement

Min Particle Displacement

Low pressureLow pressureHigh pressure

Resonant Waves in A Vibrating Column of AirL

Resonant Waves in A Vibrating Column of AirL

l = 2L

Resonant Waves in A Vibrating Column of AirL

l = 2L

Resonant Waves in A Vibrating Column of AirL

l = 2L

l = L

Resonant Waves in A Vibrating Column of AirL

l = 2L

l = L

Resonant Waves in A Vibrating Column of AirL

l = 2L

l = L

l = 2L/3

Resonant Waves in A Vibrating Column of Air

l = 2L = 2L/1

l = L = 2L/2

l = 2L/3 = 2L/3

l = L/2 = 2L/4

l = 2L/5 = 2L/5

Resonant Waves in A Vibrating Column of AirFundamental(1st Harmonic)

2nd Harmonic

3rd Harmonic

4th Harmonic

5th Harmonic

n = 1

n = 2

n = 3

n = 4

n = 5

Resonant Waves in A Vibrating Column of Air

nL2

l ,...4,3,2,1nwhere:Resonant wavelength formula

For two fixed ends and two open ends:

,...4,3,2,1nwhere:Resonant frequency formula

vLnfn

2

Resonant Waves in A Vibrating Column of AirFor tubes resonating in air the velocity will always be the speed of sound (~340 m/s)

Resonant Waves in A Vibrating Column of AirDisplacement of

MoleculesPressure Distribution(dark – high pressure)

Resonant Waves in A Vibrating Column of AirFor tubes with one end closed:

Fraction of wave

One full wavelengthL

Resonant Waves in A Vibrating Column of AirFor tubes with one end closed:

Fraction of wave

One full wavelength

¼ sineL

Resonant Waves in A Vibrating Column of AirFor tubes with one end closed:

Fraction of wave

One full wavelength

¼ sineL

4L

Resonant Waves in A Vibrating Column of AirFor tubes with one end closed:

Fraction of wave

One full wavelength

¼ sineL

4L

¾ sine

Resonant Waves in A Vibrating Column of AirFor tubes with one end closed:

Fraction of wave

One full wavelength

¼ sineL

4L

¾ sine 4L/3

Resonant Waves in A Vibrating Column of AirFor tubes with one end closed:

Fraction of wave

One full wavelength

¼ sineL

4L

¾ sine 4L/3

sine45

Resonant Waves in A Vibrating Column of AirFor tubes with one end closed:

Fraction of wave

One full wavelength

¼ sineL

4L

¾ sine 4L/3

sine45 4L/5

Resonant Waves in A Vibrating Column of Air

Trend?4L

4L/3

4L/5

Resonant Waves in A Vibrating Column of Air

Trend?4L

4L/3

4L/5 ,...9,7,5,3,1

4

nnLl

Resonant wavelength formula for one fixed end and one open end

Resonant Waves in A Vibrating Column of Air

,...9,7,5,3,1

4

nnLl Resonant

wavelength formula

For One Closed End/One Open End:

Resonant frequency formula

,...9,7,5,3,14

n

vLnfn

Resonant Waves in A Vibrating Column of AirHuman voice: