Sound Waves

Sound waves are very similar to light or electromagnetic waves. Through a homogeneous medium, sound travels at a constant speed of 343 m/s which, conveniently, is about 1 foot per millisecond. From a single source, sound radiates in spherical waves with amplitudes decrease inversely with distance. These waves are reflected by smooth surfaces and scattered by rough surfaces. A surface is “smooth” if the size of irregularities is small relative to the wavelength, and “rough” otherwise.

Sound waves are diffracted around imposing objects. If the object is small compared to the wavelength, it has very little effect meaning that the wave just passes around the object undisturbed. Otherwise, if the object is large, a “sound shadow” appears behind the object and a significant amount of energy is reflected towards the source. Lastly, if the object is about the same size as a wavelength, things are complicated, and interesting “diffraction patterns” appear.

Conveniently, sound waves follow the wave equation because the equation is linear with constant coefficients. In music a pure tone is a tone that has a sine wave when graphed. These are most often created by a tuning fork or a skilled instrumentalist. If these sine waves are from a single point and held to a constant frequency, then the reflection or other response at any other point in space is a sine wave with the same frequency as well. The only variables are the amplitude and phase changes.

There are two main types of sine waves, spatial and temporal waves. For spatial waves we define the wavelength, which is the distance of one period of the wave. In a temporal wave we define the frequency in periods per second, angular frequency in radians per second and the period itself in seconds.

Unfortunately, most natural sounds are not sine waves, because sine waves have a very narrow-band spectrum they become increasingly difficult to localize. However other wave-forms can be represented as a form of sine waves. This is using a Fourier analysis where the signal and its designated starting frequency is represented as a complex Fourier series..