These two transverse Gaussian waves are constructively interfering, an example of acoustic resonance.
The simplest demonstration of this can be performed with a long variable length tube and a speaker at one end. The condition for constructive interference is....
where L is the length of the tube, lambda is the sound's wavelength, and n is an integer corresponding to the mode. A well documented version of this experiment can be found here.
At this point you may wonder, what is a sound wave? The answer is all around you. Sound waves are nothing more than oscillations in the air around us. Sound is propagated by longitudinal compression's and rarefractions of whatever the gas particles may be. It can also be done in liquids and solids.
Because it is the medium itself responsible for the oscillations, sound cannot be made to propagate through a vacuum.
Temperature also effects how sound waves travel. The hotter the environment,
the faster they travel. The actual speed is proportional to the square
root of the temperature. Formula
relating speed to temp. The process is considered to be locally adiabatic,
therefore governed by the equation PV^y = const. where
P is pressure, V is volume, and y is a dimentionless parameter characteristic
of the gas. A complete thermodynamic treatment of sound waves can
be found here.
An interesting phenomena of acoustic resonance occurs when sound waves
pass over a cool lake. Because the waves travel in every direction
away from the source, some waves go straight across the lake while others
go up and over it. On a hot day, some of the waves that go just over
the lake will be refracted downwards and arrive at the same location as
the wave that went directly over it. The two waves will construct
a louder sound than the original source. Diagram
of waves passing over lake
Here are some other related links...
Noise
and Pleasent Sound
table
of noise intensity
Attenuation
Math
of sound waves
Aeroacoustic
resonance
By now you are an expert in Acoustic Resonance. We should be grateful
that we are able to observe all sorts of wonderful sounds with our ears.
If we could somehow see the air molecules vibrating it would be quite a
spectacle! Acoustic Resonance is nothing more than constructive interference
of sound waves.
Questions, comments: email
phonon@msn.com