Making Waves

When an oscillation disturbs something else (like water, or a slinky, or the Earth), then a mechanical wave is produced. The material that is disturbed (forced to oscillate) is called the medium.

Examples of Mechanical Waves

Some examples of mechanical waves include

• ocean waves
• sound
• earth quakes

Identify the medium for each of the mechanical waves listed above.

Further defining mechanical waves

A mechanical wave is caused by a repeating disturbance that causes energy to be passed through a medium. This movement of energy causes the particles of the medium to oscillate - but not travel - as the wave passes.

note - the wave moves to the right, but the red and blue squares do not travel with it

Classifying Mechanical Waves

A transvese wave is one where the disturbance that causes the wave is perpendicular to the direction in which the wave travels. Below are two images of transverse waves.

A longitudinal wave is one where the disturbance that causes the wave is parallel the the direction in which the wave travels. Below are two images of longitudinal waves.

Water Waves

A water wave is a mechanical wave that is both transverse and longitudinal. This up-and-down and back-and-forth motion causes a particle of water to oscillate in a circle.

Parts of a Wave

Examine the diagrams below to identify the vocabulary associated with transverse and longitudinal waves.

Electromagnetic Waves

There are a class of waves that do not need a medium through which to travel. You are familiar with most of theses kinds of waves. Examples include light, radio waves, x-rays, and microwaves. We call these electromagnetic waves. They can pass through empty space and do not disturb matter as they travel.

All of the types of electromagnetic waves have been grouped together and arranged in order of decreasing wavelength. This grouping is known as a the spectrum of electromagnetic radiation.

You can remember the order of waves in the EM Spectrum with this sentence: Real Men Insist Vehemently Upon eXtra Gravy.

The Visible Spectrum

Visible light, including all the colors of the rainbow, are just a tiny part of the electromagnetic spectrum.

White light is actually a mixture of all the colors of the rainbow. If we pass white light through a prism we can split it up into its colors, as shown below.

The Rainbow

As mentioned earlier, the visible spectrum is just a part of the larger electromagnetic spectrum, as shown below.

You can remember the order of the colors of light in the visible spectrum by remembering this name: ROY G. BIV - red, orange, yellow, green, blue, indigo, violet - arranged from lowest to highest frequency.

Further Characteristics of EM Waves

• Where mechanical waves require the vibration of matter for propogation, EM waves are the propogation of electrical and magnetic force fields.
• The electrical and magnetic force fields oscillate perpendicular to each other and they are both perpendicular to the direction of wave travel.
• The EM fields are created by the acceleration of charged particles.
• Both fields are in phase (they reach their maximum and minimum (zero) at the same point in time).
• In a vacuum, all EM waves travel at the same speed, known as the speed of light,
  c = 3.0×10⁸m/s.

Describing Waves

Waves can be described mathematically using a combination of algebra, trig and geometry. The notes that follow give you the vocabulary you will need when you get to the math later on.

wave front

A wave front is a line drawn that represents the position of the crest of a wave at a point in time. It is a tool for representing a 3-D wave in 2-D. A diagram showing a number of successive wave fronts can be used to determine the wavelength of a wave.

ray diagram

A ray is a line with an arrow showing the direction of travel of a wave. It cannot be used to find wavelength or frequency. A ray diagram is usually used for showing the path of light waves as they reflect off mirrors or pass through lenses. Consider the ray diagram below showing how to locate the image of an object in a flat mirror. The diagram shows the rays leaving the candle, reflecting off the mirror, and reaching an observer.

displacement-position graph

If you were to take a picture of a wave on a rope at an instant in time, you would get a picture that looks like a sine curve. It shows the displacement of each point on the rope at that single instant in time. At some other point in time you would get a different curve. The graph below on the right is a displacement-position graph for the wave at the time of 27 seconds. From a displacement-position graph you are able to determine wavelength and amplitude, but not time period or frequency.

displacement-time graph

A displacement-time graph shows the displacement of a single point on the wave as a function of time. The graph on the left above shows the displacement of the red dot as time passes. From this type of graph you can find time period, frequency and amplitude, but not wavelength.

The Wave Speed Equations

mechanical waves	electromagnetic waves
v = λ × f	c = λ × f

The speed of a wave is the speed at which the energy is transferred. For mechanical waves, speed is represented with the symbol v. Light slows down as it passes through a medium. It moves slower in water, for example, than it does in air.

For electromagnetic waves, we use the symbol c. All electromagnetic waves move at this speed, known as the speed of light. In a vacuum, the speed of light is equal to, c = 3×10⁸m/s.

Wave speed is measured in meters per second, m/s.

Wave speed is mathematically related to two measurable factors: wavelength and frequency.

The wavelength of a wave is the length of one complete cycle of the wave - often measured from peak (crest) to peak, or from trough to trough. Wavelengths are measured in meters, and they are represented by the Greek letter lambda, λ.

The frequency of a wave represents the number of complete waves that pass a fixed point each second. Frequency is represented by the letter f and is measured in units of 1/s (per seconds), which is sometimes called a hertz (Hz).

The speed of a mechanical wave is determined by the characteristics of the medium it is travelling through, and not by the disturbance that makes the wave. The speed of a wave in a rope, for example, is determined by the type of material the rope is made of and the tension in the rope, and not by how hard the person shakes the rope. Whether the rope is shaken fast or slow, the speed of the wave produced is the same.

Follow this link to explore the effects of a disturbance on the characteristics of a mechanical wave.

Large disturbances produce large amplitiudes. Fast disturbances produce small wavelengths. Large or small, fast or slow, the speed does not change.

There is a mathematical relationship between wave speed, v, wavelength, λ,and time period, T.

The more common form of this equation uses frequency instead of time period.

Example 1 - Water Waves

• Question
• a)
• b)

Example 2 - What note?

• Question
• Answer

Example 3 - Illuminated Wavelengths

• Question
• Answer