WAVES-Formations of waves in different medium

WAVES-Formations

OPEN PIPE: Open pipe: A pipe open at both ends is called an open pipe.

When a sound wave hits a wall, it is partially absorbed and partially reflected.  A person far enough from the wall will hear the sound twice.  This is an echo.

In a small room, the sound is also heard more than once,

but the time differences are so small that the sound just seems to loom.  This is known as reverberation.

PITCHES

Music is the sound that is produced by instruments or voices.  To play most musical instruments you have to create standing waves on a string or in a tube or pipe.

The perceived pitch of the sound is related to the frequency of the wave.  The higher the frequency, the higher is the pitch.

Wind instruments: produce sounds by means of vibrating air columns.  To play a wind instrument you push the air in a tube with your mouth or a reed.  The air in the tube starts to vibrate with the same frequency as your lips or the reed.  Resonance increases the amplitude of the vibrations, which can form standing waves in the tube.  The length of the air column determines the resonant frequencies.  The mouth or the reed produces a mixture of different frequencies,

but the resonating air column amplifies only the natural frequencies.  The shorter the tube the higher is the pitch.  Many instruments have holes, whose opening and closing controls the effective pitch.

We can create a standing wave in a tube, which is open on both ends, and in a tube,

which is open on one end and closed on the other end.  Open and closed ends reflect waves differently.  The closed end of a tube is an antinode in the pressure (or a node in the longitudinal displacement).  The open end of a tube is approximately a node in the pressure (or an antinode in the longitudinal displacement)

Tubes with  open ends

The longest-standing wave in a tube of length L with two open ends has displacement antinodes (pressure nodes) at both ends.
This is also known as fundamental or first harmonic.

TUBES WITH CLOSED ENDS

The next longest-standing wave in a tube of length L with two open ends is the second harmonic.
It also has displacement antinodes at each end.

An integer number of half-wavelength has to fit into the tube of length L.

L = nλ/2,  λ = 2L/n,  f = v/λ  = nv/(2L).

For a tube with two open ends all frequencies f_n = nv/(2L) = nf₁, with n equal to an integer, are natural frequencies.

In Conclusion:

Thus, the harmonics in an open pipe are in the ratio of natural numbers.