Mechanical waves are a disturbance through a medium. While all mechanical waves must move through a medium, a wave is not a physical object, but a disturbance which transmits energy.
Waves can be either transverse or longitudinal. A transverse wave oscillates particles perpendicular to its direction, while a longitudinal wave oscillates particles in the direction it transmits energy. These waves form areas of high and low pressure as crests and troughs, also called antinodes, but behave in the same way.
The above graphic is a position-position graph, which describes the actual shape of the wave. However, waves also move through a medium at some constant speed. A position-time graph of a wave looks similar, but instead of a wavelength (lambda, distance), the distance (on the graph it represents time) between crests is the period (T, time) in seconds.
The speed of the wave can be represented as the product of its wavelength and its frequency, or the quotient of its wavelength and its period. However, Changing either one of these values does not affect wave speed, as the speed of a wave is dependent on the material through which it travels. The speed of a wave through a string is the square root of the tension of the string over it's linear mass density, or:
v = (Ts/μ)^.5
v = (Ts/μ)^.5
Because waves are not matter, multiple waves can occupy the same space at the same time. This is called interference. When waves interfere, their amplitudes will add or subtract depending on the phase of the wave. This is called constructive and destructive interference respectively.
For example, waves in a pond will interfere to create a pattern of crests and troughs where the waves add and subtract with each other:
https://www.youtube.com/watch?v=lpee2Qddqjo
When two sound waves have similar frequencies, they can create a beat frequency. This is when the two waves gradually shift in and out of phase to form a new frequency which is the difference between the two original frequencies.
https://www.youtube.com/watch?v=pRpN9uLiouI
When a wave encounters a boundary, or a change in medium, some of the wave will be reflected back, some of the wave will continue through the new medium, and some will be converted into heat energy.
https://www.youtube.com/watch?v=c5JfH-rCC_A
Standing waves are waves which appear to be stationary. However, standing waves are created by waves traveling across the length of an object and reflecting back at a certain speed so that the interference of the wave and its reflection create the appearance of a stationary wave. Standing waves only occur when objects oscillate at a certain frequency, called a resonant frequency. Different resonant frequencies are called harmonics. oscillating an object at different harmonic frequencies will yield different numbers of nodes and antinodes as well as pitches.
Because standing waves are made from traveling waves, they will be affected by the tension and the linear density of the medium through which they travel. For example, if a string forming a standing wave stretches, the tension will change and the standing wave will no longer form.
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