Unit 1.1 Wave Quantities
Quantities that describe a periodic or Continuous Wave
λ — Wavelength — distance between successive crests or troughs. Measured in metres (m).
Α — Amplitude — height of the crest or depth of the trough. Measured in metres (m).
Т — Period — time between passage of successive crests or troughs. Measured in seconds (s).
f — Frequency — number of crests (or troughs) passes per unit time. Measured in Hertz (Hz) or inverse seconds (s^{1}). Period and frequency are inverse quantities!
Τ = ^{1}/_{f}  Eq 1
v — Wave velocity — is the speed at which wave crests (or any other fixed point on the wave shape) move forward. The wave speed must be distinguished from the speed of a particle of the medium itself. Partilces in a medium may actually be moving back and forth or side to side or up and down, etc. but the energy of the wave moves forward with its velocity v.
A wave crest travels a distance of one wavelength, in a time equal to one Period.
Using the equation of motion: velocity = ^{distance}/_{time}.
v = ^{λ}/_{Τ}
Substituting for T we get v = fλ  Eq. 2
Example 1
A water wave with crests 6m apart pass by a buoy, every 2.0 s. Calculate the (a) frequency, (b) period, (c) wavelength and (d) velocity of the wave.
Information given
– Period is 2s (time between successive crests)
 wavelength is 6m (distance between successive crests)
(a) f = ^{1}/_{Τ}
Frequency = 0.5 Hz (which is actually s^{1}).
(b) Period = 2.0s (given as time between successive crests).
(c) Wavelength λ = 6m (given as distance between successive crests).
(d) Velocity v = fλ or v = ^{λ}/_{Τ} then velocity is 3ms^{1}.
Example 2:
Based on the diagram above, calculate the (a) frequency, (b) period, (c) wavelength.
Information given – Velocity is 1 ms^{1}; wavelength is 1m (distance between successive crests).
(a) Frequency f = ^{v}/_{λ}
f = 1.0 Hz (which is actually s^{1}).
(b) Period Τ = ^{1}/_{f}
Τ = 1.0s (given as time between successive crests).
(c) wavelength λ = 1 m (given as distance between successive crests).
Exercise 1.1.4
1. What is a wave?
2. What is transferred along the direction of wave motion?
3. Consider the variables frequency, wavelength, period and amplitude. Which of these are (a) space properties of waves? (b) time properties of waves?
4. A vibrating loose exhaust in my car has a frequency of 3000 Hz. Calculate the following properties of the sound produced: (a) period (b) If the wave speed is 330 ms^{1}, what is the wavelength?
