Wave speed equation
The speed of a wave is related to its The number of waves produced each second. The unit of frequency is hertz (Hz). and The length of a single wave, measured from one wave peak to the next., according to the equation:
\(wave~speed~ = frequency \times wavelength \)
\(v = f~ \lambda\)
where:
v = wave speed in metres per second, m/s
f = frequency in hertz, Hz
\(\lambda\) = wavelength in metres, m
All waves, including sound waves and electromagnetic waves, follow this equation.
Some waves have their own specific speeds:
- the speed of light and all electromagnetic waves in a vacuum is 300,000,000 m/s or 3×108 m/s
- the speed of sound in air is often taken to be 340 m/s.
Example
What is the speed of a water wave that has a frequency of 0.5 Hz and a wavelength of 3 m?
v = f λ
f = 0.5 Hz
λ = 3 m
v = 0.5 × 3
v = 1.5 m/s
The speed of the wave is 1.5 m/s
Question
A sound wave has a frequency of 10 kHz and a wavelength of 3.4 cm. What is its speed?
v = f λ
The frequency is 10 kHz.
This must be converted to Hz to be used in the equation.
f = 10 kHz = 10,000 Hz
The wavelength is in cm.
This must be converted to m to be used in the equation.
λ = 3.4 cm = \(\frac{\text{3.4}}{\text{100}}\) = 0.034 m
v = 10,000 × 0.034
v = 340 m/s
The speed of the wave is 340 m/s.
Question
A radio wave has a frequency of 3 MHz and a speed of 300,000,000 m/s. What is its wavelength?
v = f λ
v = 300,000,000 m/s
f = 3 MHz = 3 x 106 Hz
300,000,000 = 3 x 106 x λ
λ = \(\frac{\text{300,000,000}}{\text{3 x 10}^6}\)
λ = 100 m
The wavelength of the radio wave is 100 m.