Wavelength, frequency, amplitude and time period

Describing a wave

To tell two sounds apart we need numbers. Four quantities describe a sound wave.

Wavelength

The wavelength, $\lambda$, is the distance between two neighbouring compressions (or two rarefactions), in metres. On a graph of pressure against distance, it is the distance from one crest to the next.

Frequency

The frequency, $f$, is the number of complete waves (vibrations) passing a point each second, in hertz: $1\ \text{Hz}$ is one wave each second.

Time period

The time period, $T$, is the time for one complete vibration, in seconds. More waves each second means less time for each one:

Amplitude

The amplitude is the biggest change of pressure (or of the particle's position) from its normal value. A bigger amplitude carries more energy.

You should find that doubling the frequency halves the time period and doubles the number of waves in $20\ \text{ms}$. The amplitude changes the height of the waves only.

Watch out. Change milliseconds to seconds before you use $f = \dfrac{1}{T}$: $4\ \text{ms} = 0.004\ \text{s}$.

A worked example

A microphone graph shows $7$ complete waves in $14\ \text{ms}$. Find the time period, the frequency and the wavelength in air.

1. Time period. $T = \dfrac{14\ \text{ms}}{7} = 2\ \text{ms} = 0.002\ \text{s}$.
2. Frequency. $f = \dfrac{1}{0.002\ \text{s}} = 500\ \text{Hz}$.
3. Wavelength. $\lambda = \dfrac{340\ \text{m/s}}{500\ \text{Hz}} = 0.68\ \text{m}$ (from the next lesson's $v = f\lambda$).

Practise with new numbers

Try it in Python

The program finds the time period of several notes.

Remember these

• Wavelength $\lambda$: compression to compression, in metres.
• Frequency $f$: waves each second, in hertz.
• Time period $T = \dfrac{1}{f}$: the time for one wave.
• Amplitude: the size of the pressure change.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. A source vibrates $125$ times in $1\ \text{s}$. What are its frequency and time period?

2. The time period of a wave is $0.02\ \text{s}$. What is its frequency?

3. Does a sound of higher frequency have a longer or a shorter time period?

4. A sound of $30\ \text{kHz}$ is played. Can a person hear it?