# Progressive Waves

Progressives waves are oscillations produced by the transfer of energy from one place to another. They differ from stationary waves in that they progress (move) on the material that propagates them.

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Figure 1. Ocean waves are an example of progressive waves.

The oscillations made by the waves crests and troughs move from one place to another. You can think of these movements as the propagation or progression of the wave from point A to point B. The crests are the point of maximum height, while the troughs are the waves lowest point.

## The properties of progressive waves

As progressive waves move from one point to another, undulations will repeat if the waves are being produced constantly. The four main characteristics of a progressive wave are its wavelength, period, frequency, and velocity.

### The wavelength of progressive waves

This is defined as the length from the beginning to the end of the wave.

Figure 2. The wavelength is the total length of a wave cycle from beginning to end. Source: Manuel R. Camacho, StudySmarter.

The wavelength of a progressive wave is related to its energy. The amount of energy differs depending on the nature of the wave. In ocean waves, smaller wavelengths indicate waves with low energy, while in electromagnetic waves, shorter wavelengths indicate larger energies.

### The period of progressive waves

As waves move from one point to another, the pattern will repeat if the oscillation does not change. The time it takes for the pattern of oscillation to pass through one point is called the period, which is better defined as the time between two crests or troughs. It is measured in seconds.

Figure 3. The time it takes for a wave to move between the points that mark its beginning and end (green dots) is the wave period. This can be calculated as the time difference between moments t1 and t2: t2-t1 = T. Source: Manuel R. Camacho, StudySmarter.

### The velocity of progressive waves

If we divide the wavelength by the wave period, we get the time it takes for the wave to advance. This is the wave velocity, which is measured in m/s.

$c = \frac{\lambda}{t}$

### The frequency of progressive waves

The inverse of the wave period tells us how long it takes for the wave to repeat itself in one second. If the frequency is 1, it takes 1 second for the wave to repeat itself. If it is lower than 1, the wave is faster. If it is greater than 1, the wave is slower. The frequency is the inverse of the period, and it is measured in Hertz.

$f = \frac{1}{T}$

### The cycle of progressive waves

The complete pattern of a wave from crest to trough is called a wave cycle. Its speed is linked to the wave frequency and velocity.

## How do we measure the properties of progressive waves?

To measure the properties of a progressive wave, we need a reference point. The properties related to wavelength and wave height need reference points on the horizontal and vertical axes. To measure the properties related to wave cycles, we need to take the time it takes for the wave to move from one point to another.

### Measuring the wavelength and wave height

To measure the wavelength, we need to fix a point on the horizontal axis. To simplify this, we can take a crest, which is easiest to identify (as we said earlier, the crest and trough represent the waves maximum and minimum heights). Measuring the distance between two consecutive maximums, we get the wavelength.

Figure 4. The distance from crest to crest gives us the wavelength. Source: Manuel R. Camacho, StudySmarter.

$\lambda = \text{distance between points}$

To measure the wave height, we need to measure the distance between the crest and trough, as shown below.

Figure 5. The wave height is the distance between the crest and trough or the waves maximum and minimum heights. Source: Manuel R. Camacho, StudySmarter.

$H = Max - Min$

Half the distance between the crest and the trough gives us the wave amplitude.

$Amplitude = \frac{H}{2}$

### Measuring the wave period and frequency

To measure properties related to the wave cycle, we need to measure the time it takes for the wave to move from one point to another. Again, we need to select a fixed point, with the crest or trough being the best options.

If we measure the time it takes from one crest or trough to the next, we obtain the wave period.

Figure 6. The time difference between A and B (two crests) gives us the wave period. We need to measure the difference from tb to ta, or $$T = tb-ta$$. Source: Manuel R. Camacho, StudySmarter.

## Examples of progressive waves

Progressive waves occur in nature when an object oscillates and produces waves that move through space. The space can be a liquid, gas, solid, or a vacuum.

• Waves moving through a liquid, e.g., ocean waves, which are generated by the wind.
• Waves moving through a gas, e.g., sound moving through the air.
• Waves moving through a solid, e.g., mechanical waves moving in the ground after an earthquake.
• Waves moving through a vacuum, e.g., electromagnetic waves such as the light coming from the sun.

Interestingly, electromagnetic waves, seismic waves, wind waves, and sound waves can all be found in the sea, which is a medium that propagates many forms of waves.

## Progressive Waves - Key takeaways

• A progressive wave is a wave that moves from one position to another.
• Progressive waves have properties such as wavelength, height, amplitude, velocity, frequency, and period.
• Examples of progressive waves are sound waves, seismic waves, and ocean waves.
• Some properties such as wave height, wave amplitude, and wavelength depend on the dimensions of the wave.
• Properties such as wave period, velocity, and frequency depend on the time it takes for the wave to complete one cycle.

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What is a progressive wave?

A progressive wave is a wave that moves from one point to another.

What is the difference between a progressive and a stationary wave?

Progressive waves move from one point to another whereas stationary waves do not. Respective examples are ocean waves (progressive) and the vibrations of a guitar string (stationary).

How do we measure the wavelength and wave period?

To measure the wavelength, we need to measure the distance between two consecutive maximums (crests).

By measuring the time it takes from one crest to the next, we obtain the wave period.

## Test your knowledge with multiple choice flashcards

What is a progressive wave?

Which waves can move through a vacuum?

What are the crests and troughs of a wave?

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