# Wave Speed

Wave speed is how fast a wave travels from one place to another, carrying energy as it goes. The speed of a wave depends on its frequency ('f') and wavelength ('λ'). This is important because it tells us how quickly the wave spreads through the medium that carries it. For example, in the ocean, waves travel through water, while sound waves travel through the air. The type of wave and the characteristics of the medium also affect the wave's speed. This is why wave speed is an important concept to understand when studying waves. Specifically, when discussing waves, wave speed is a crucial factor to consider.

## How to calculate wave speed

Calculating wave speed requires two pieces of information: the wavelength and the frequency of the wave. We can use the formula below to find it. Frequency is measured in Hertz, while wavelength is measured in meters.

Wavelength, symbolized by the Greek letter lambda (λ), is the total length from one crest to the next, as seen in Figure 2. Meanwhile, frequency, symbolized by the letter f, is the inverse of the time it takes for a crest to move to the position of the next one.

Another way to calculate wave speed is by using the wave period ‘Τ’, which is defined as the inverse of the frequency and provided in seconds.

This gives us another calculation for wave speed, as shown below:

## The period of a wave is 0.80 seconds. What is its frequency?

Wave speed can vary, depending on several factors, not including the period, frequency, or wavelength. Waves move differently in the sea, the air (sound), or in a vacuum (light).

### Measuring the speed of sound

Sound waves are a type of mechanical wave that travels through a medium, including fluids and solids. The speed of sound changes depending on the density of the medium it travels through. This means that sound can faster through materials like water air, where it moves slower as density is lower.

In gases like air, the speed of sound also depends on the temperature, density, and even the humidity. At average conditions of 20°C and at sea level, sound moves at a speed of 340.3 m/s. We can calculate the speed of sound in the air by dividing the distance travelled, symbolized by 'd', in meters by the time difference, symbolized by 'Δt'.

Scientists use the speed of sound in the air at average conditions as a reference for objects traveling at high speeds. This is measured using the Mach number, which is the object's speed 'u' divided by 'v', the speed of sound in the air at average conditions.

As the temperature increases, so does the speed of sound in the air. This is because heat in a gas is the average value of the energy in the air molecules, which increases their velocity. Faster-moving air molecules vibrate more quickly, making it easier for sound waves to travel through them. For instance, at 0°C and sea level, the speed of sound is about 331 m/s, which is about 3% slower than at average conditions.

### Measuring the speed of water waves

Wave speed in water waves is different from that of sound waves. In this case, the speed depends on the depth of the ocean where the wave propagates. If the water depth is more than twice the wavelength, the speed will depend on the gravity ‘g’ and the wave period, as shown below.

In this case, g = 9.81 m/s at sea level. This can also be approximated as:

If waves move to shallower water and the wavelength is larger than twice the depth ‘h’ (λ > 2h), then wave speed is calculated as follows:

As with sound, water waves with larger wavelengths travel faster than smaller waves. This is the reason why large waves caused by hurricanes arrive at the coast before the hurricane does.

Here is an example of how the speed of waves differs depending on the depth of the water.

A wave with a period of 12sIn the open ocean, the wave is not affected by the water depth, and its velocity is approximately equal to v = 1.56 • T. The wave then moves to shallower waters with a depth of 10 metres. Calculate by how much its speed has changed. Wave speed ‘Vd’ in the open ocean is equal to the wave period multiplied by 1.56. If we substitute the values in the wave speed equation, we get: The wave then propagates to the coast and enters the beach, where its wavelength is larger than the depth of the beach. In this case, its speed ‘Vs’ is affected by the beach depth. The difference in speed is equal to the subtraction of Vs from Vd. As you can see, the speed of the wave decreases when it enters shallower waters.

As we said, the speed of waves depends on the depth of the water and the wave period. Larger periods correspond to larger wavelengths and shorter frequencies.

Very large waves with wavelengths reaching more than a hundred meters are produced by large storm systems or continuous winds in the open ocean. Waves of different lengths are mixed in the storm systems that produce them. However, as the larger waves move faster, they leave the storm systems first, reaching the coast before the shorter waves. When these waves reach the coast, they are known as swells.

Water waves have a different speed than sound waves, and their speed depends on the depth of the ocean where they propagate. If the depth of the water is more than twice the wavelength of the wave, the speed of the wave depends on gravity 'g' and the wave period. If the wavelength is larger than twice the depth, waves moving to shallower water have a different speed calculated using a different

### The speed of electromagnetic waves

Electromagnetic waves are different from sound waves and water waves, as they do not require a medium of propagation and thus can move in the vacuum of space. This is why sunlight can reach the earth or why satellites can transmit communications from space to earth base stations.

Electromagnetic waves move in a vacuum at the speed of light, i.e., at approximately 300,000 km/s. However, their speed depends on the density of the material they are passing through. For instance, in diamonds, light travels at a speed of 124,000 km/s, which is only 41% of the speed of light.

The dependence of the speed of electromagnetic waves on the medium they travel in is known as the refractive index, which is calculated as follows:

Here, ‘n’ is the index of refraction of the material, ‘c’ is the speed of light, and ‘v’ is the speed of light in the medium. If we solve this for the speed in the material, we get the formula for calculating the speed of electromagnetic waves in any material if we know the refractive index n.

The following table shows the light velocity in different materials, the refractive index, and the material’s average density.

The values for air and water are given at standard pressure 1 [atm] and a temperature of 20°C.

As we said and is illustrated in the table above, the speed of light depends on the density of the material. The effect is caused by the light impacting atoms in the materials.

Wave speed is a critical factor in understanding how waves propagate in a medium. The medium itself can be anything from vacuum solid, and the speed of the wave depends on its frequency or wavelength. In the sea, we observe that lower frequencies lead to faster wave propagation.

Electromagnetic waves, which travel at the speed of light, can be slowed down in denser mediums. This is because the density of the medium causes the waves to encounter more atoms, which absorb and release photons, creating a time delay.

The speed of ocean waves depends on their period and the depth of the water. When waves move to shallower waters, the speed of the wave changes, and its wavelength becomes larger than the depth of the water. This results in a decrease in wave speed as the wave moves from deeper to shallower waters.

Similarly, the speed of sound traveling through the air depends on the air temperature. Colder temperatures cause sound waves to move more slowly, while warmer temperatures allow sound waves to propagate more quickly.

In summary, wave speed is an essential concept in understanding how waves propagate in different mediums. The wavelength, frequency, and properties of the medium all play a role in determining wave speed.

## Wave Speed

What speed do electromagnetic waves travel at?

Electromagnetic waves travel at the speed of light, which is approximately 300,000 km/s.

How do we calculate wave speed?

Generally, the speed of any wave can be calculated by multiplying the wave frequency by its wavelength. However, the speed can also depend on the density of the medium as in electromagnetic waves, the depth of the fluid as in ocean waves, and the temperature of the medium as in sound waves.

What is wave speed?

It is the speed at which a wave propagates.

What is wave speed measured in?

Wave speed is measured in units of velocity. In the SI system, these are metres over second.