Wave speed measures the distance a wave travels within a period of time. It depends on two other factors – wavelength and wave frequency.
The exact speed of most waves will vary depending on the medium – i.e., substance – that it is traveling through, which varies from solids, liquids, and gases. But not all waves are created equal.
This article will explain how wave speeds differ, how to calculate them, and how it’s measured.
Wave speed is measured in meters per second (m/s) because it is the unit of measurement in the International System of Units (SI) for speed and velocity.
Since wave speed measures the distance traveled by a wave over a given time period, it follows the basic formula for speed which is:
- Speed = Distance / Time
As such, the SI unit for distance is meters (m), and the SI unit for time is seconds (s), resulting in the unit for speed as meters per second.
Wave speed can be calculated by multiplying the wave frequency (f) by wavelength (λ). Therefore, you can use the following formula:
- Wave speed (v) = frequency (f) x wavelength (λ)
v – measured in meters per second (m/s)
f – measured in Hertz (Hz)
λ – measured in meters (m)
Frequency (f)
Frequency is the number of waves that pass by a given point every second.
It is measured using the SI unit Hertz (Hz), named after a German physicist who was the first person to broadcast and receive radio waves.
To calculate frequency, you can use the following formula:
- f = 1 / T
T = The time it takes for one wave to pass a certain point.
You can also use another formula:
- f = n / T
n = The total number of waves that pass by a given point
T = The time it takes for those waves to pass by that given point
Wavelength (λ)
Wavelength is the distance between two identical points on two waves next to each other. For example, the distance between two peaks of adjacent waves would be its wavelength.
It is measured using the SI unit meters (m).
To calculate wavelength, you can use the following formula:
- λ = v / f
v = The wave’s speed
f = The wave’s frequency
There is an inverse relationship between wavelength and wave frequency. As you increase the wavelength, its wave frequency decreases. As you increase frequency, its wavelength decreases.
Now that we know what wave speed is, how it’s measured, and its relationship between wavelength and frequency, we can use this information to calculate it relative to the other measurements. Let’s take a look at a few examples.
How to calculate wave speed from wavelength and frequency
Suppose you want to calculate the speed of a wave that has a frequency of 30 Hz and a wavelength of 4 m. Simply substitute these values into the wave speed formula:
- Wave speed (v) = frequency (f) x wavelength (λ)
- Wave speed = 30 Hz x 4 m = 120 m/s
- Wave speed = 120 m/s
How to calculate wavelength from wave speed and frequency
Suppose you want to calculate the wavelength of a wave traveling at 7 m/s at a frequency of 3 Hz. First, you would rearrange the wave speed equation to make it a function of wavelength:
- Wave speed (v) = frequency (f) x wavelength (λ)
- Wavelength (λ) = wave speed (v) / frequency (f)
- Wavelength = 7 m/s / 3 Hz
- Wavelength = 2.33 m
How to calculate frequency from wave speed and wavelength
Suppose you want to calculate the wave frequency of a wave traveling at 36 m/s with a wavelength of 8 m. You would rearrange the wave speed equation to make it a function of wave frequency:
- Wave speed (v) = frequency (f) x wavelength (λ)
- Frequency (f) = wave speed (v) / wavelength (λ)
- Frequency = 36 m/s / 8 m
- Frequency = 4.5 Hz
In practice, measuring wave speed depends on whether you’re measuring water waves, sound waves, or electromagnetic waves. Let’s explore this in more detail.
Measuring the speed of water waves
The speed of water waves depends on how deep the water is. If the water depth is more than double the wavelength, the wave speed will depend on gravity and the time period in which it’s measured. As such, the speed of an ocean wave can be calculated as follows:
- v = (g / 2π) x T
g = gravity at sea level (9.81 m/s)
T = Time
Since g = 9.81 and 2π = 6.283, we can simplify the equation to:
- v = 1.56 x T
When the wave moves toward the shore where the water is shallower and the wavelength becomes larger than twice the water depth, you would use a different formula:
- v = √(g x λ)
It should be noted that waves with larger wavelengths move faster than smaller wavelengths. Therefore, waves in the open ocean typically move faster than waves closer to the beach.
Measuring the speed of sound waves
The wave speed of sound works differently than water waves. This is because a sound wave travels through a medium, such as through solids like walls and gases like air. These sound waves will travel faster through more dense mediums such as solids and water than they will through gases.
Through the air, the wave speed can be calculated as follows:
- v = d / Δt
d = distance traveled in meters
Δt = the difference in time
The wave speed of sound through air depends on the temperature, humidity, and density of the air. As such, the formula mentioned above can be used to measure sound speed in average conditions, which is defined as a temperature of 20°C and at sea level. This results in a wave speed of 340.3 m/s.
Measuring the speed of electromagnetic waves
Electromagnetic waves are a different type of wave than the previous two. Electromagnetic waves travel through a vacuum of space at the speed of light, but their speed can vary depending on how dense the material it’s passing through is. For instance, through space, electromagnetic waves travel at around 300,000 km/s, but through glass, it travels at 200,000 km/s.
This is known as the refractive index, which can be calculated as follows:
- n = c / v
n = Refraction index of the material
c = speed of light
v = speed of light in the medium
Therefore, if you want to calculate the speed of electromagnetic waves through any medium with a known refraction index, you can rearrange the equation as follows:
- v = c / n
Wave speed is the distance a wave travels within a given time period, and it is measured with the unit meters per second (m/s). It is calculated by using the equation ‘Wave speed = frequency x wavelength’.
Calculating wave speed in practice depends on whether you’re measuring water waves, sound waves, or electromagnetic waves, all of which have their own unique formula.
