 Resource Lesson Wave Fundamentals
A wave is defined as the transfer of energy from one point to another. There are two large, all encompassing categories of waves: mechanical and non-mechanical.

Mechanical waves are waves that require a medium for the transfer of their energy to occur. Water waves are an example of mechanical waves. Tsunami waves released after an earthquake transfer the energy of the quake to distant shorelines. Sound waves are another type of  mechanical wave. They are compression waves that have a frequency between 20-20000 hertz and travel through dry air at an speed of approximately 340 m/sec at room temperature. Different substances carry compression waves at various speeds; metals carry it faster than water which transfers it faster than air. As a mechanical wave travels through a medium, it loses energy to the medium. The molecules in the medium are forced to vibrate back and forth, generating heat. Consequently, the wave can only propagate through a limited distance. When this event happens, we say that the wave has been damped. Damping can be observed by the fact that the wave's amplitude has decreased.

Non-mechanical waves are waves that do not require a medium for the transfer of their energy to occur. Electromagnetic waves are the only type of non-mechanical waves. They can travel through the vacuum of space. Light from distant stars travel hundreds of thousands of millions of years to reach us. Although the electromagnetic radiation spans a large spectrum of wavelengths and frequencies, all electromagnetic radiation travels through a vacuum at 3 x 108 m/sec, or c, the speed of light.

Type of radiation Range of wavelengths
570 down to 2.8 meters
TV
5.6 down to 0.34 meters
microwave
0.1 down to 0.001 meters
10-3 down to 10-7 meters
visible light
 red orange yellow green blue indigo violet
700 to 400 nm
ultraviolet
10-7 down to 10-10 meters
x-rays
10-10 down to 10-12 meters
gamma rays
shorter than 10-12 meters

Within these two large categories, there are four principle types of waves:
• Transverse waves are waves in which the particles vibrate at right angles to the direction of the wave's velocity or propagation. An example of this type of wave would be pulses traveling along a string as it is being shaken. Transverse waves can be polarized since their vibrations can be constrained, or restricted, to move in only one plane. Acoustics Animations © Dr. Dan Russell, 1999 The above animation was created using a modified version of the  Mathematica ® Notebook "Sound Waves" by Mats Bengtsson.

 Amplitudes of transverse waves are measured in terms of their heights, or distance above/below their undisturbed equilibrium positions. • Longitudinal waves are waves in which the particles vibrate parallel to the direction of the wave's velocity, or direction of propagation. Sound waves are a prime example of this type of wave. Acoustics Animations © Dr. Dan Russell, 1999 The above animation was created using a modified version of the  Mathematica ® Notebook "Sound Waves" by Mats Bengtsson.

 Amplitudes of longitudinal waves are measured in terms of the increase or decrease in pressure in the medium as the wave travels.Compressions are regions of high pressure; while rarefactions are regions of reduced pressure. • Elliptical waves, or surface water waves, result when longitudinal and transverse behaviors are superpositioned, or overlap, as they pass through the same medium simultaneously. Note the behavior of the two blue particles identified by Dr. Russell. Each particle travels in a clockwise circle as the wave passes from left to right. Acoustics Animations © Dr. Dan Russell, 1999
• Torsional waves can only occur in physical structures; for example, bridges and building. These wave cause the structures to vibrate by twisting about a central axis. Below you can see a snapsot of the Tacamo Narrows suspension bridge, in Washington state, as it began vibrating in November, 1940. The bridge collapsed less than three hours later at 11 AM. picture courtesy of Carleton University video: Tacoma Narrows Bridge

When examining waves, information is usually displayed in two types of graphs, vibration graphs and waveform graphs. The shapes of both types of graphs are the identical; the only difference is in the labels for the x-axis. A vibration graph (or history graph) displays the behavior at a SINGLE location in the medium as the wave passes. Its x-axis is labeled as time. One vibration can be defined as one complete cycle, or back and forth motion. A waveform graph (or snapshot graph) displays the behavior of a multitude of locations in the medium at a SINGLE moment in time. Its x-axis is measured in terms of distance.  Vibration graphs inform the reader of the wave's shape, amplitude, and period. While waveform graphs inform the reader of the wave's shape, amplitude, and wavelength.
The amplitude, A, is the wave's maximum disturbance from it undisturbed equilibrium position and represents the energy being transferred by the wave. Generally, the energy of a mechanical wave is proportional to the square of the wave's amplitude; i.e., if a wave's amplitude triples, its energy content will become 9-times greater.

On a vibration graph, the period, T, is the time between two adjacent in-phase points on a vibration graph. The reciprocal of period is frequency, f. It represents the numbers of waves that pass a given location each second along the wave's path.

 period frequency time required for only ONE vibration total number of vibrations EACH second sec/vib (or just) seconds (sec) vib/sec (or just) hertz (hz)

All wave motion is generated by a source that moves or vibrates. Consequently, the frequency of a wave is a property of its source, not of the medium through which its energy subsequently travels.

On a waveform graph, the wavelength, λ, is the distance between two adjacent in-phase points on a waveform graph.  A crest is a point of  maximum positive amplitude along the wave while a trough is a point of maximum negative amplitude.

 property vibration(history) waveform(snapshot) wave shape yes yes amplitude yes yes period yes no wavelength no yes
A wave is either periodic, shown as a sinusoidal pattern that repeats itself at regular intervals; or it is a single, one-time disturbance called a pulse. The examples shown in the problems below are periodic in nature.

Applying the kinematics equation d = rt, we can derive the equation for a wave's speed. Since the distance that a wave travels in one period is its wavelength, we can substitute as follows,

d = rt
λ = vwT
vw = λ / T
vw = fλ

Remember that the frequency of the source determines the frequency of the wave. When traveling through the same medium, high frequency waves have short wavelengths, while low frequency waves have longer wavelengths - that is, frequency and wavelength are inversely proportional, not reciprocals.

Two points are said to be in-phase if they behave exactly the same; that is, if they are a multiple of a wavelength apart. If two points are not in-phase, then they are out-of-phase . Since a wavelength corresponds to one complete vibration, or one complete revolution, one wavelength is often expressed as 360º.  So in-phase points are separated by n360º. Out-of-phase points can be any number of degrees apart. Although we usually speak of points which are separated by 90º, 180º, or 270º.

Refer to the following information for the next five questions. Using point A as a reference, what point(s) is 90º out-of-phase?

 Using point A as a reference, what point(s) is 180º out-of-phase?

 Using point A as a reference, what point(s) is 270º out-of-phase?

 Using point A as a reference, what point(s) is 360º in-phase?

 Using point A as a reference, what point(s) is 720º in-phase?

Refer to the following information for the next five questions. Using point F as a reference, what point(s) is 90º out-of-phase?

 Using point F as a reference, what point(s) is 180º out-of-phase?

 Using point F as a reference, what point(s) is 270º out-of-phase?

 Using point F as a reference, what point(s) is 360º in-phase?

 Using point F as a reference, what point(s) is 630º out-of-phase?