Wave period and wave speed
The time period of a wave can be calculated using the equation:
\(time \ period = \frac{1}{frequency}\)
\(T = \frac{1}{f}\)
This is when:
- time period (T) is measured in seconds (s)
- frequency (f) is measured in hertz (Hz)
Example
Calculate the time period of a wave with a frequency of 5 Hz.
\(T = \frac{1}{f}\)
\(T = 1 \div 5\)
\(T = 0.2~s\)
Question
Calculate the time period of a wave with a frequency of 400 Hz.
\(T = 1 \div 400\)
\(T = 0.0025~s\)
Calculating wave speed
Wave velocity, the speed of a wave, can be calculated using the equation:
wave speed = frequency × wavelength
\(v \ = f \ \lambda \)
This is when:
- wave speed (T) is measured in metres per second (m/s)
- frequency (f) is measured in Hertz (Hz)
- wavelength (λ ) is measured in metres (m)
Example calculation
What is the wave speed if the frequency is 50 Hz and the wavelength is 6 m?
\(v \ = f \ \lambda \)
\(v \ = 50 \times 6 \)
\(v \ = 300 \ m/s \)
Question
What is the speed of a wave with a frequency of 0.2 Hz and a wavelength of 25 m?
\(v \ = f \ \lambda \)
\(v \ = 0.2 \times 25 \)
\(v \ = 5 \ m/s \)
The speed of sound in different materials
Sound is a mechanical longitudinal wave. The wave is passed on by collisions between particles, so the speed the wave moves depends on the density of the particles.
| Medium | State | Speed of sound |
| Steel | Solid | 6,000 m/s |
| Water | Liquid | 1,500 m/s |
| Air | Gas | 330 m/s |
| Medium | Steel |
|---|---|
| State | Solid |
| Speed of sound | 6,000 m/s |
| Medium | Water |
|---|---|
| State | Liquid |
| Speed of sound | 1,500 m/s |
| Medium | Air |
|---|---|
| State | Gas |
| Speed of sound | 330 m/s |
When sound moves from one A material through which a wave can be transmitted (propagate). into another, the change in speed will also cause a change in wavelength, frequency is unaffected.
wave speed = frequency × wavelength
Constant frequency means that the wavelength will be proportional to the wave velocity.
