Wave Properties

There are two main types of waves: longitudinal and transverse. In a longitudinal wave, the disturbances at each point are parallel to the direction of wave transmission(also known as propagation). In a transverse wave, the disturbances at each point are perpendicular to the direction of wave propagation. Combined waves, like water, are a mix between the two which means that each point or particle moves in a circular motion whose direction depends on the wave's propagation. If the wave goes left, the point oscillates counterclockwise. If the wave goes right, the point oscillates clockwise.

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It's important to know that the wave doesn't push the point particles in the direction of propagation. In transverse waves, the particles only create disturbances up and down. In longitudinal waves, the particles only create horizontal disturbances. In mechanical waves, a little bit of both happens.

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If you're a math enthusiast or have experience with trigonometry, you'll know the functions f(x) = sin(x) and f(x) = cos(x) in the Cartesian plane are waves. So, you will likely heard many of the terms applied to waves as terms for trigonometric graphs. This allows for many wave-based phenomena to be easily modeled by sine and cosine.

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The following transverse water wave image visualizes the succeeding concepts below. In real life, of course, water waves are actually combination waves.

The amplitude of a wave can be considered as how much the wave moves up and down in a single oscillation. Visually, the amplitude of a wave is half the difference between its crests and troughs -- the distance between the equilibrium point to the extreme points.

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As a general rule of thumb, the intensity of a wave is proportional to the amplitude of the wave squared. This relationship is easier to visualize in a harmonic oscillator but becomes somewhat misconstrued in more complex waveforms, with multiple variables at play, making the proportionality not usually 100% accurate. However, the proportionality remains intact: the amplitude of a wave and its intensity are directly related. For waves that follow the square proportionality, it's as simple as this. If you double the wave's amplitude, you quadruple its intensity.

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In sound, amplitude refers to volume. In light, it refers to brightness. For a seismic wave, it's how "strongly spread out" the earthquake is, which isn't a desirable trait. These are examples of the physical implications of wave amplitude

The wavelength of a wave is exactly what it sounds like. It's effectively how long one cycle of the wave is. This can be seen as the distance between successive crests and troughs, or really any two adjacent identical parts of a wave. Wavelength is measured usually in meters(m). Wavelength is usually denoted by lower-case lambda(λ).

The period of a wave is defined as the time it takes for the wave to complete one cycle. In a more relatable scenario, let's imagine you have a swing. If you pull it back all the way and release, the time it takes for the swing to come back to the same spot you released it at would be the period of the swing. Note that the period of a wave-like motion like this isn't just based on location. It's based on how you get there too. For example, if I ran one lap around a track, the time it took for me to run that lap is like the period: it's the time it takes for one cycle to complete.

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The inverse of the period of a wave is its frequency, measured in 1/seconds, or hertz(hz). The frequency on its own is essentially how "frequently" a cycle occurs. You can kind of imagine it in units of cycles per second(how many cycles or oscillations does the system go through in a given time interval).

The velocity of a wave is just like any other velocity: it's how fast the wave is propagating through space. However, this velocity is not the same as the oscillation speed of the particles moving up and down(or left and right if the wave is longitudinal). These particles don't really have a valuable displacement since they periodically return to the same position. Also, the particles of the medium that the wave travels through don't travel at the same speed as the wave itself.

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The phase velocity is dependent on the medium the wave travels through and that medium's linear mass density. This relationship becomes more easily quantified when you investigate standing waves on a string.

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As we know, velocity is measured in m/s usually. If you notice, wavelength is measured in meters, and frequency is measured in hertz or 1/s. If you notice, these three quantities have very similar units that we can connect. The connection is extremely simple to make. You take your wavelength(in meters) and multiply it by frequency(1/s) to get velocity(m/s), giving us the wave-speed equation.

As seen, you can express this equation in terms of period, too, since the period is the inverse of frequency.

As seen, you can express this equation in terms of period, too, since the period is the inverse of frequency.

What if two waves met each other?

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The answer to this question is a lot simpler than you think. It's as simple as this: the amplitudes of the waves add up. In real life, you've probably seen this before when two water waves collide. The two water waves form a larger wave with a greater height than either of the initial two waves, demonstrating the principle of wave superposition. This also works for negative amplitudes.

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If this doesn't make sense, think about in terms of a function. If we took f(x) = sin(x) and a g(x) = cos(x), and superposed(or added) them together, you get a function with a larger amplitude than either sin(x) or cos(x). At each and every point on this superposed waveform, the amplitude is the sum of the amplitudes of the two constituent waves. After the waves pass, they go back to their original waveforms.

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If a wave enters a new medium, part of the wave will be transmitted and the other part will be reflected. The other part will invert if the new medium is harder to move in than the initial medium.

If a wave hits an end that is free to move vertically, the wave will reflect but not invert. If the end is rigid and in place, the waveform will invert and reflect. This is because the force the wave exerts on the end will be counteracted by an opposite force on the wave, flipping it, due to Newton's Third Law.

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If a wave enters a new medium, part of the wave will be transmitted and the other part will be reflected. The other part will invert if the new medium is harder to move in than the initial medium.