Acoustic Resonance

       Have you ever passed by a lake and heard the loud "ribbet" sounds that frogs make and wonder to yourself, how do those little frogs make such a loud noise?  Well it's not any individual frog that makes that loud noise.  Because all the frogs produce the "ribbet" at nearly the same frequency and wavelength, the sound becomes amplified.  To see details of a wave click here
            The purely classical concept of acoustic resonance is very simple to understand.  When sound waves travel through air, with a definite wavelength, they are subject to interfere with other sound waves.  If both waves have comparable wavelengths, the interference is constructive, otherwise it is destructive.   The wave itself is produced from any vibrating object. Resonance

            These two transverse Gaussian waves are constructively interfering, an example of acoustic resonance.

 Animation of longitudinal wave of air molecules

            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