The Eighth Grade science teacher said, ‘Students today we will be going over waves, grab a partner and make sure that you take good notes. A wave is an example of periodic motion. We have already learned that a period is a length or portion of time and that motion is the action or process of moving or being moved. Waves are constructed from the particles of a specific medium which oscillate back and forth about a fixed position. The time which it takes for such a particle to complete one full cycle is known as the period. Boys please stop laughing, as this is not meant to be funny.
Anyways, period units are simply seconds (or minutes or hours or days or years or some time unit). The frequency of a wave describes the number of complete cycles which are concluded during a given period of time. This makes frequency a rate quantity (ratio between two related quantities) which describes the rate of oscillations or vibrations or cycles or waves on a per second basis. Think about your heart beating and it can speed up or slow down at different times (running faster, sleeping slower) because it is a heart rate. The quantity frequency is often confused with the quantity period. Period refers to the time that it takes to do something. When an event occurs repeatedly, then we say that the event is periodic and refer to the time for the event to repeat itself as the period. Frequency and period are distinctly different, yet related, quantities. Frequency refers to how often something happens. Period refers to the time it takes something to happen. Frequency is a rate quantity. Period is a time quantity. Frequency is the cycles/second. Period is the seconds/cycle.
A common unit of frequency is the Hertz, abbreviated as Hz. Do not think about the Rent-A-Car company, as this Hertz comes from a German physicist named Heinrich Rudolf Hertz. A Hertz indicates the number of complete cycles per second. There is a mathematical relationship between the frequency (f) of the wave and the period (T) of the wave as denoted by the following relationship: f = 1 / T. Once you know the frequency, then it is easy to calculate the period, and vice versa as they are opposites of each other. Frequency refers to how many waves are made per time interval. This is usually described as how many waves are made per second, or as cycles per second.
There are many different types of waves, but for this lesson I want all of you to think about sound waves, string waves or water waves. Waves originate from vibrations, which are oscillating motions over a fixed position. A vibration can cause a disturbance to travel through a medium, transporting energy without transporting matter. Wave Parameters (period, frequency, amplitude, speed and wavelength) are the ways in which we measure waves. A wave can be drawn on the Cartesian coordinates that you learned about in Math class featuring both the X and Y axes. This allows us to plot the wave as a function of time so we are able to examine that the portion of a wave between two crests or troughs which is called a wave cycle. Everyone look at the projection shown on the screen illustrating the wave cycle.
Now we will learn about wavelength, which is a property of a wave that most people (once they know what to look for) can spot quickly and easily, and use it as a way distinguishing between different waves. The part of any wave which has the maximum Y value or upward displacement rising to a peak is called a crest. Any part that is sloping down like a valley is a trough. Wavelength is defined as the distance from a particular height on the wave to the next spot on the wave where it is at the same height and going in the same direction. It is a measure of horizontal length. There is no need to start at the crest or trough on the wave to measure wavelength, just make sure you are back to the same height going in the same direction. Although most normal people measure from one crest to the next crest (or trough to trough), just because they are easy to spot. Wave height, normally refers to the distance from the bottom of the trough up to the peak of a wave. Amplitude is measured from the resting position to the peak. Amplitude is the maximum positive displacement of the medium from its undisturbed position (X axis) to the top of a crest.
Considering sound waves, wavelength affects the pitch of the sound, as the closer together the waves are, the higher the tone sounds. A Loud wave would have a high amplitude and a High Pitched wave would have a high frequency. Loudness refers to the Amplitude of the wave or how high up on the Y axis it is. A wave which has a large amplitude (so when drawn its waves would be very high) would sound very Loud. Pitch refers the Frequency of the wave, which means how many waves per second. A sound wave with a high Frequency/Pitch would sound like a high-pitched squeal and its waves would be packed very close together. Loudness means quantity of energy and amplitude while pitch is quantity of frequency. Loudness is directly proportional to wave amplitude or the intensity of wave, whereas pitch is directly proportional to frequency and inversely proportional to intensity of waves. I hope you are all taking good notes on this as there will be a quiz tomorrow.
If you go to the beach and watch an ocean wave moving along the medium (the ocean water), you should be able to observe that the crest of the wave is moving from one location to another over a given interval of time. The crest will eventually disappear into the distance. The speed of an object refers to how fast an object is moving and is usually expressed as the distance traveled over time. In the case of a wave, the speed is the distance traveled by a given point on the wave (such as a crest) in a given interval of time. The equation for wave speed has the following formula, speed = distance divided by time.
After a wave passes through a medium, there are no residual effects; the medium remains unchanged. For example, if you throw a stone in a pond, a circular wave will spread out from the point of impact. If the wave encounters an object floating in the water, the object will briefly bob up and down. However, once the wave has passed, the object, and the water that buoys it up, will be left undisturbed. Some waves, such as sound and water waves, require a material medium. On the other hand, light and other forms of electromagnetic radiation can travel through the vacuum of space. A fascinating feature of waves is that two of them, traveling in opposite directions, can pass right through each other and emerge with their original identities. However, while the pulses overlap, the height at any point is simply the sum of the displacements due to each pulse itself. If the pulses are on the same side of the medium they add; if they are on opposite sides, they subtract. This is called interference.
The principle of superposition may be applied to waves whenever two (or more) waves travelling through the same medium at the same time. The waves pass through each other without being disturbed. The net displacement of the medium at any point in space or time, is simply the sum of the individual wave displacements. This is true of waves which are finite in length (wave pulses) or which are continuous sine waves.
Sometimes when you vibrate a string, or cord, or chain, or cable it’s possible to get it to vibrate in a manner such that you are generating a wave, but the wave doesn’t propagate. Wave propagation refers to the ways in which waves travel. The wave just sits there vibrating up and down in place. This type of a wave is called a standing wave. Waves that propagate are traveling waves. Traveling waves have high points called crests and low points called troughs (in the transverse case) or compressed points called compressions and stretched points called rarefactions (in the longitudinal case) that travel through the medium. Standing waves don’t go anywhere, but they do have regions where the disturbance of the wave is quite small, almost zero. These locations are called nodes. There are also regions where the disturbance is quite intense, greater than anywhere else in the medium, called antinodes. Standing waves don’t form under just any circumstances. They require that energy be fed into a system at an appropriate frequency. That is, when the driving frequency applied to a system equals its natural frequency. This condition is known as resonance. Standing waves are always associated with resonance. Resonance can be identified by a dramatic increase in amplitude of the resultant vibrations. Compared to traveling waves with the same amplitude, producing standing waves is relatively effortless. Class, that is all I have for you today and Bobby please stop fidgeting with that spinner.’