Back to P6 Home
P6 B) Wave Speed & Time
P6 B) Wave Speed & Time
Wave Speed Equation
The frequency of a wave is the number of full/ complete waves that pass through a certain point each second. Frequency is measured in hertz (Hz) where 1 Hz is one full wave per second. Frequency is also measured in kilohertz (1 KHz = 1 thousand Hz), megahertz (1 MHz = 1 million Hz) or gigahertz (1 GHz = 1 billion Hz).
The wavelength is the length of a full cycle of a wave.
We can calculate the speed of a wave by multiplying the frequency (number of full waves per second) by the wavelength. The calculation and formula triangle for this is shown below.
The frequency of a wave is the number of full/ complete waves that pass through a certain point each second. Frequency is measured in hertz (Hz) where 1 Hz is one full wave per second. Frequency is also measured in kilohertz (1 KHz = 1 thousand Hz), megahertz (1 MHz = 1 million Hz) or gigahertz (1 GHz = 1 billion Hz).
The wavelength is the length of a full cycle of a wave.
We can calculate the speed of a wave by multiplying the frequency (number of full waves per second) by the wavelength. The calculation and formula triangle for this is shown below.
For this equation, velocity is measured in metres per second (m/s), frequency is measured in hertz (Hz) and wavelength is measured in meters (m).
Example 1
A wave has a frequency of 80 Hz and a wavelength of 0.4 metres. Find the speed of the wave.
We work out the speed of the wave by multiplying the frequency (f) by the wavelength (λ).
A wave has a frequency of 80 Hz and a wavelength of 0.4 metres. Find the speed of the wave.
We work out the speed of the wave by multiplying the frequency (f) by the wavelength (λ).
The question tells us that the frequency is 80 Hz and the wavelength is 0.4 metres; we sub these values into the formula.
Therefore, the speed of the wave is 32 m/s.
Example 2
A wave has a frequency of 12 Hz and a speed of 36 m/s. Find the wavelength.
We find the calculation that we undertake to find the wavelength by covering up wavelength (λ) in the formula triangle. When we do this, we see that we find the wavelength by dividing the speed (v) by the frequency (f).
A wave has a frequency of 12 Hz and a speed of 36 m/s. Find the wavelength.
We find the calculation that we undertake to find the wavelength by covering up wavelength (λ) in the formula triangle. When we do this, we see that we find the wavelength by dividing the speed (v) by the frequency (f).
The question tells us that the speed is 36 m/s and the frequency is 12 Hz. These values are in the correct units, so we sub them into the calculation.
Therefore, the wavelength is 3 metres.
Example 3
Both of the previous examples have been fairly straight forward because all of the values were in the correct units. We are now going to have an example whereby the values are not in the correct units. For this question, we need to remember that 1 kilohertz (KHz) is 1 thousand Hz, 1 megahertz (MHz) is 1 million Hz and 1 gigahertz (GHz) is 1 billion Hz.
Question
A wave has a frequency of 2.9 MHz and a wavelength of 37 cm. Find the speed of the wave.
We find the speed of the wave by multiplying the frequency (f) by the wavelength (λ).
Both of the previous examples have been fairly straight forward because all of the values were in the correct units. We are now going to have an example whereby the values are not in the correct units. For this question, we need to remember that 1 kilohertz (KHz) is 1 thousand Hz, 1 megahertz (MHz) is 1 million Hz and 1 gigahertz (GHz) is 1 billion Hz.
Question
A wave has a frequency of 2.9 MHz and a wavelength of 37 cm. Find the speed of the wave.
We find the speed of the wave by multiplying the frequency (f) by the wavelength (λ).
Frequency is measured in hertz and wavelength is measured in metres. The question tells us that the frequency is 2.9 MHz. There are 1 million hertz in 1 MHz, so we convert 2.9 MHz to Hz by multiplying by 1,000,000 (or by 106); the frequency is 2,900,000 Hz (2.9 x 1,000,000). The question also tells us that the wavelength is 37 cm. There are 100 cm in 1 metre, so we convert 37 cm to metres by dividing by 100; the wavelength is 0.37 m (37 ÷ 100). We now sub the frequency and wavelength into the calculation.
The speed of the wave is 1,073,000 m/s.
Time Period
The time period is the amount of time that it takes for one full cycle of the wave. We can find the time period of the wave by dividing 1 by the frequency.
The time period is the amount of time that it takes for one full cycle of the wave. We can find the time period of the wave by dividing 1 by the frequency.
Frequency is measured in hertz and time is measured in seconds.
We can also find the frequency by dividing 1 by the time period.
We can also find the frequency by dividing 1 by the time period.
Here is the formula triangle.
Example 1
A wave has a frequency of 20 Hz. Find the time period.
We find the time period for a wave by dividing 1 by the frequency. The question tells us that the frequency is 20 Hz, so we divide 1 by 20.
A wave has a frequency of 20 Hz. Find the time period.
We find the time period for a wave by dividing 1 by the frequency. The question tells us that the frequency is 20 Hz, so we divide 1 by 20.
Therefore, the time period for the wave is 0.05 seconds.
Example 2
The time period for a wave is 0.000125 seconds. Find the frequency of the wave. Give your answer in KHz.
We find the frequency of the wave by dividing 1 by the time period. The question tells us that the time period is 0.000125.
The time period for a wave is 0.000125 seconds. Find the frequency of the wave. Give your answer in KHz.
We find the frequency of the wave by dividing 1 by the time period. The question tells us that the time period is 0.000125.
The frequency of the wave is 8,000 Hz. The question asks us to give the frequency in kilohertz (KHz) rather than hertz (Hz). There are 1,000 hertz in a kilohertz, so we convert Hz to KHz by dividing by 1,000.
The frequency of the wave is 8 KHz.