Definition: Wave

A wave consists of energy passing through a medium. The speed at which a wave moves is determined by the type of wave and the medium it is traveling through. The primary determining factor is the medium. For example, the speed of sound through air is different than the speed of sound through liquid. Wave speed is one of the primary characteristics of a wave.

The second primary characteristic of a wave is its wavelength. A wave is characterized by regions of high energy and low energy and the distance between the peaks (highest energy) and troughs (lowest energy) within that wave determine its wavelength. For example, a high-pitched sound has a short wavelength meaning that if you took a picture of the air compressions of a volume of air as a high-pitched sound wave was passing through that wave, you would see that the points of highest compression (peaks) would be close together compared to a picture of a lower-pitched wave.

The observed wavelength/frequency of any wave gives us its characteristic feature. The wavelength of sound gives us its pitch with pitch rising as the wavelength decreases.

Frequency is another term associated with waves and is effectively the inverse of wavelength. When a wave is observed or measured, it vibrates an object and the number of vibrations per second (or other unit of time) determine its observed characteristic. For example, with sounds our ears to not measure the wavelength of a sound wave. Rather, a sound wave vibrates our eardrum some number of times per second and that frequency of vibration is translated into pitch, the characteristic feature of sound.

Observation of a wave frequency is a determined by the speed of the wave and the wavelength of the wave.

Math  

Frequency (f) is the observed (measured) number of peaks per second (p/s).

Wavelength (w) is the observed distance between 2 wave peaks (p/d).

Wave Speed (s) is the distance a peak moves in a second (d/s).

f = w*s

The frequency (number of peaks per second) is equal to the wavelength (distance between peaks) times the wave speed (distance the peaks travel every second).

A “note” is the music term for some frequency of sound wave as observed by the ear. The more often a peak is observed, the higher the frequency. This means that a short sound wave moving through a medium that makes it go slow can sound the same as a long wavelength sound wave in a medium that makes it go fast.

All that is measured by the ear is the frequency.

Light is another type of wave and it is the one that most important to astronomy. It too has wavelength and frequency and the speed of light depends on the density of the object it is passing through. For example, light travels fastest in a vacuum (complete absence of matter) and slower in denser substances like light and glass.

Light comes in packets of electro-magnetic energy called photons and photons can come in many different wavelengths as described by the electro-magnetic spectrum. The shortest wavelength photons are gamma rays. As the wavelengths of photons get higher they are categorized as X-Rays, Ultra Violate (UV) Rays, Visible Light, Infra-Red (IR), Microwave, and Radio Waves.

The biological engineering in human eyes allow us to see visible light because the cones and rods within our eyes are agitated by certain wavelengths of photons and send neuron impulses to our brains in response to these agitations.

The rainbow is an electro-magnetic spectrum of visible light. We can see from red to violate on a rainbow due to the engineering of our eyes but if we could see longer or shorter wavelengths then a rainbow might look much different.

Red photons are the longest photons humans can see which is why it is at one end of the rainbow. Violate photons are the shortest wavelength we can see which is why it is at the other end of the rainbow. Notice that Infra-Red (IR) is the set of wavelengths that begins at the wavelength a little longer than the red we can see and Ultra-Violate (UV) set of wavelengths begins at the wavelength a little shorter than those we can see.

All photons are made of the same “stuff” (oscillating electro-magnetic fields) and the main thing that makes visible light special to humans is the biological engineering of our eyeballs.

Definition: Emission Wavelength (EW)

Each wave has a moment of emission. At this moment of emission the emission process determines the wavelength of the wave.

For example, if you pluck a guitar string or strike a piano key the vibrating string creates a vibration in the air that corresponds to a “note” of some frequency. Once emitted, that compression wave with its frequency will travel through the air for some period of time before reaching the ear of someone listening.

The characteristics of the medium influence the wavelength of the wave. For example, a musician will need to tune a guitar differently for environments of different humidity or elevation because the speed of sound changes based on the conditions of the air. A note might sound the same in different environments but the compression wave in the air will be moving faster or slower depending on the density of the air so the emission wavelength will have to be different in the different environments in order for the hearer to hear the same note due the speed of the wave. 

The Wave Emission involves only that moment at which the wave was emitted. Each wave has an Emission Wavelength (EW).

Definition: Observed Frequency (OF)

When a wave is observed (or measured) only its frequency can be measured. The wave’s energy is absorbed by the measuring device and the frequency of the wave is the only piece of information that the observer can directly measure. The wavelength of the wave can be calculated based on the speed of the wave and the frequency of the wave, but the Emission Wavelength (EW) of the wave is impossible to directly measure.