Topic 5. General properties of waves

There are two ways to view a wave: either as the disturbance in all of space at a single instant in time or as the disturbance as a function of time at a single point in space. In the first view, we would plot the magnitude of the wave disturbance at the given instant of time as a function of a distance coordinate and in the second view we would plot the magnitude of the wave disturbance at a given point in space as a function of time. Both of these pictures look the same except for the labels and units on the x-axis.

A transverse wave has its disturbance perpendicular to its direction of propagation. Waves on a string, electromagnetic waves and water waves are transverse.

A longitudinal wave has its disturbance along the long of its direction of propagation. Sounds waves are longitudinal – the pressure fluctuations of the wave are in the same direction as the wave travels.

Amplitude: Maximum displacement of wave quantity relative to the undisturbed, equilibrium position.

(height of water wave, pressure of sound wave, maximum electric field, etc.)

The Intensity of a wave or the power radiated by a source are proportional to the square of the amplitude.

Frequency: Number of cycles per second of the wave quantity, measured in Hertz (cycles per second), kHz, MHz, etc..

The frequency is usually represented by the letter n (nu) and occasionally by the letter f. The observation of the frequency is made at a single point in space.

Wavelength: Distance between corresponding points on successive cycles (e.g., between wave crests).

Measured in units of length (e.g., meters, nano-meters)

The wavelength is usually represented by the letter l (lambda).

A measurement of the wavelength is made by observing the wave in space at a single instant of time.

Period: Time between successive wave crests. Measured in units of time (e.g., seconds).

The period is often represented by the letter T. The period is measured by observing the wave displacement at a single point in space.

Phase: The time at which a wave passes through a specified displacement at a specified point in space. A common specification is the time at which the wave disturbance is exactly zero and moving in the positive direction. Although there are some applications for the absolute specification of phase, it is more common to speak of the phase difference between two waves. Although this difference can have any value in principle, the two situations we will usually encounter in this course are: (1) two waves that are exactly in phase – that is the maxima and minima of the two waves occur at exactly the same instants of time and (2) two waves that are exactly out of phase – that is the maximum of one wave occurs at the same instant as the minimum of the other. Phase differences can be measured in units of time, but are more commonly measured in fractions of a cycle. Two waves that are in phase have a phase difference of exactly 0, while two waves that are exactly out of phase have a phase difference of exactly one-half of a cycle.

Velocity of propagation: Speed of wave in space. Measured in units of speed (e.g., meters/second, km/s, etc.)

The velocity of propagation is usually a characteristic of the medium and the type of wave – it does

not depend on the parameters of the source or the detector.

The velocity of light in vacuum is usually represented by the letter c. The velocity of light in some medium other than

a vacuum (such as air) or the velocity of some other kind of wave is usually represented by v. However, we will sometimes

use c in this case as well, to avoid confusing between the velocity v and the frequency n.

Polarization: The direction of the wave disturbance in space. An electromagnetic wave that is “vertically polarized” has

its electric field vector oscillating vertically (from straight up to straight down). A wave that was “horizontally

polarized” would have its electric field vector oscillating horizontally (from right to left). Intermediate states

of polarization between purely vertical and purely horizontal are also possible. These cases are often identified

by the angle of the wave quantity with respect to the vertical axis.

The following relationships are true for all waves:

nl=c (product of wavelength and frequency equals velocity of propagation)

n= 1/T

T= 1/n (frequency and period are reciprocals of each other)

Be careful to use a consistent set of units when using these relationships. The safest method is to convert all velocity and distance quantities to meters/second or meters and all time-based quantities to seconds or Hz, removing any metric prefixes that may be present. The velocity of light can be taken to be 3x10⁸ m/s in all calculations. You should remember that this number is not exactly correct, but it is close enough for most purposes.

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