Physics 11 : Waves and Motion

Vibrations periodically repeat itself and stays wihin a set of boundaries or limits. Those limits are measured to one or another extreme from the center point or equilibrum position or rest position. We talk about the displacement from one position to the other position. Amplitiude represents the maximum displacement relative to the equilibrum position from either extreme.

The time it takes to repeat is coined as a period. That periodic repetition is called a cycle. The period is the time it takes for one cycle; the number of cycles completed in a second is called the frequency measured in hertz.

(one place in vibration to another)

There are different kinds of vibrations which are called modes.

The kind of motion manifested by a pendulum is back and forth. The technical term for that is called tranverse. When the structure is vibrating is in its rest position and the motion is pepndicular to axis of that vibrating structure; thats tranverse.

When the motion is parallel to the axis of the vibrating structure, it is called a longitundinal.

Or you can have vibration which is around the axis of the vibrating structure or a rotation vibration; which is called a torsional vibration where the motion rotates around the axis of the vibrating structure. You can have a structure which was torsionally vibrating, transversly and longitudinally vibrating at the same time.

Water is what we call a dipolar molecular, and you can make that molecular transverly vibrate by externally exciting. If you do so, it vibrates at 2.45 billion repetitions per second. That is so called its resonante frequency, when it does so it gets really warm. Thats how a microwave works by providing a frequency of extenrally applied energy and that frequency that water really likes and produces alot of heat. So theres all kind of technology that might not be inherently intuitive.

You can use different springs, or amount of masses, different length pendulums, or have different mass distributions there are various methods of controlling the frequency of the vibration.Every vibration has one thing in common and that is that most structures don't vibrate unless you encourage them to do so by work and add some energy and that's exactly what happens with the creation tsunami The launching of enormous disturbance that transfers the energy through the medium (Water) at enormous speeds from the gravitation energy released from a fault.

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Periodic back and forth movement - refer to as vibrating source, it has an amplitude and occurs at some frequency. And that frequency is measured in hertz, and that means it has a certain periodicity; as this vibration starts to increase, energy is added to the spring which is distrubted along the string and in the time the source goes from -> to ---> and that time is determined by the nature of the spring in itself. Negative and positive amplitude, the amplitude of the wave is determined by the amplitude of the source. This moves at some speed V ^- this distance from here to here <-- ! > is the length of the wave that is created by the vibration which the distance from one part of the wave to the same point of the next wave is represented algebretically by lamba whichs tands for wavelength. T is the time for one repetition or one cycle of the source to repeat.

v = Delta D / Delta T (Delta D = one wavelength when Detla T is one period)

Lamba * 1/v because 1 over period is the same as frequency.

Vibrations (Section 7.1, p. 328-333)

A vibration is a repeated pattern of motion of an object in a regular time interval, also called periodic motion. When describing vibrations, the following quantities are useful:



The amplitude of the vibration is the maximum displacement of the object from its rest position, in any direction. Symbol - A. Unit - metre (m).

The period of the vibration is the time taken to complete each full cycle of motion. Symbol - T. Unit - second (s).

The frequency of the vibration is the number of cycles completed in one second. Note that this is the mathematical inverse of period. Symbol - f. Unit - Hertz (Hz). 1 Hz = 1 cycle per second.

Waves (Section 7.2, p. 334-343)

A wave is a transfer of energy through a medium (material) without net movement of the medium itself. Waves are caused by vibrations. Examples include waves on springs, on the surface of water, or sound waves in air. When describing waves, the following quantities are useful:

The amplitude of the wave is the maximum displacement of any particle of the medium from its rest position. The wave’s amplitude is set, at least initially, by the amplitude of the source vibration. Wave amplitude tends to decrease over time because of energy losses in the medium. Symbol - A. Unit - m.

The period of the wave is the time required for one complete wave cycle to pass any given location in the medium. Wave period is always the same as the period of the source vibration. Symbol - T. Unit - s.

The frequency of the wave is the number of complete wave cycles that pass any location in the medium in one second. Wave frequency is always the same as the frequency of the source vibration. Symbol - f. Unit - Hz.

The wavelength of the wave is the distance travelled by the wave during one period. On springs or water waves, it is the distance between successive crests or successive troughs. Symbol – λ (lambda). Unit - metre (m).

Most waves can be classified as either transverse waves or longitudinal waves. A transverse wave is one in which the particles of the medium vibrate perpendicular to the direction of the wave motion. Examples include waves on springs and water waves. A longitudinal wave is one in which the particles of the medium vibrate parallel to the direction of the wave motion. An example is sound waves.

The kinematics of wave motion can be described with a variation of the constant speed equation, v = ∆d / ∆t During a time of one period (T), a wave travels a distance equal to one wavelength (λ). The speed equation therefore becomes: v = λ / T Since period is the mathematical inverse of frequency, T = 1 / f, or f = 1 / T. The speed equation can therefore also be written in this form: v = f λ This is known as the Universal Wave Equation, and applies to all types of waves.

Wave Interference (Section 7.3, p. 344-352)

When two waves travel through the same space at the same time, they cause temporary interference. The displacement of any particle in the medium will be equal to the sum of the displacements that would have been caused by each component wave independently. Wherever the two waves affect the medium in the same direction, the result is a larger displacement than normal, called constructive interference. Wherever the two waves affect the medium in opposite directions, the result is a smaller displacement than normal, called destructive interference. While interfering, the resultant wave shape can be quite different from the originals, but once the two waves are past each other, they are unchanged from their original form.

If two identical waves travel through each other in opposite directions, the resulting pattern is a special case of interference known as a standing wave. Complete destructive interference, called nodes, will occur every one-half wavelength along the pattern. The medium remains stationary at these locations. Halfway between each node are places of maximum constructive interference, called antinodes. The amplitude of vibration at these locations is double the amplitude each component wave.

Physics Grade 11 Folder - Waves and Motion