The wave equation
The wave equation is a very important formula that is often used to help us describe waves in more detail.
\(Wave\,speed = frequency \times wavelength\)
\(v = f \times \lambda\)
Where Wave speed is in metres per seconds (\( m\,s^{-1}\))
Frequency is in Hertz \((Hz)\).
Wavelength is in metres \((m)\).
NB:
It should be noted that some particular waves have their own specific speeds.
The speed of light and all of the other waves in the EM spectrum is \(300,000,000 m\,s^{-1}\) or \(3\times 10^{8}m\,s^{-1}\).
The speed of sound in air is \(340 m\,s^{-1}\).
The speed of light and sound changes in different materials. Please check carefully which speed to use in the data sheet on page 2 of the question paper.
Examples
Example 1
Question
What is the speed of a water wave that has a frequency of \(0\cdot 5Hz\) and a wavelength of \(3 m\)?
\(v = ?\)
\(f=0\cdot 5\,Hz\)
\(\lambda = 3\,m\)
\(\Rightarrow v = f \times \lambda\)
\(\Rightarrow v = 0\cdot 5 \times 3\)
\(\Rightarrow v = 1\cdot 5\,m\,s^{-1}\)
This formula can be used for any speed including the speed of light.
Example 2
Question
What is the wavelength of a radio wave transmitting at \(98.3 MHz\)?
It looks like there is only one piece of information in the question but it says that the wave is a radio wave and all radio waves (and EM waves) travel at the speed of light – \(3 \times 10^{8}m s^{-1}\).
\(v = 3 \times {10^8}\,m\,s^{-1}\)
\(f = 98\cdot 3MHz = 98\cdot 3 \times {10^6}Hz\)
\(\lambda = ?\)
\(v = f \times \lambda\)
\(\Rightarrow 3 \times {10^8} = 98\cdot 3 \times {10^6} \times \lambda\)
\(\Rightarrow \lambda = 3 \times {10^8} \div 98\cdot 3 \times {10^6}\)
\(\Rightarrow \lambda = 3\cdot 05m\)