Sound

Wavelengths and Frequencies in Tubes

Standing waves:

  • (a) A sealed pipe. The dark blue regions are at density or pressure antinodes.
  • (b) The fundamental mode.
  • (c) The second harmonic at the instant a positive peak is at x=1/4 2.
  • (d) The direction of motion of the molecules at that moment.
  • The associated pressure, which is 90o out-of-phase with the displacement represented in (c).

The condition for standing wave is that 2L = n , where n = 1, 2, 3, . . .



Open tubes

A few standing-wave modes for an organ pipe open at both ends. The arrows show the direction in which air moves for half the cycle, whereupon the mode reverses. Both ends of the tube are at atmospheric pressure and there are pressure nodes at both.

Standing sound waves in a tube:

Anti nodes at ends

Condition: n = 2/n * L , for n = 1, 2, . . .

All harmonics are produced.

Closed tubes (one end open, one end closed)






A few standing-wve modes for an organ pipe open at its lower end. The arrows who the direction in which air moves for half the cycle, whereupon the modes reverse. The dashed lines indicate the displacement nodes and antinodes.
All brass instruments are closed at one end by the mouth of the player.

Anti nodes at one end

Condition: n = 4/(2n-1) * L , for n = 1, 2, . . .

Only ODD harmonics are produced.

Standing waves in open tubes

Standing waves in closed tubes

Summary

(Tubes)



all harmonics

only odd harmonics

Wave Velocity: v = 20.1 ( T ) 1/2

T is the Kelvin temperature of air in tube.

Remember: Room temperature is 292 K

Frequency : ( v = * f )

n = 1, 2, 3, 4, . . .n = 1, 3, 5, . . .

"Standard" pitch: A = 440 Hz

lower pitch: ---> smaller frequency

higher pitch: ---> higher frequency

Some Definitions in Sound Science

Wave Term Colloquial
amplitude = loudness
frequency = pitch
attenuated = damped

Sound travels at known velocity.

Speed of sound in Air :

v = 342 m/s
at room temperature (292 K)

Sound travels faster in warmer air

Sound travels slower in cooler air

Water

v = 1500 m/s
at 292 K

Reflection, Diffraction, Absorption and Refraction of Sound

Reflection: the sound can bounce from a "stiff" barrier (echo).

Diffraction: the sound can bend around a barrier.

Absorption: the sound can be absorbed by materials.

Refraction: sound can "bend" due to different air temperatures

(remember demonstration where a wave front of water wave was bent due to different depths of the ripple tank. Examlpe for sound: Ship horn in fog can be heard a longer distance due to temperature variations in the air.)

Ch. Elster
Aug 26 14:27:03 EDT 2019