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Vibrations and Waves. They are All Around!!!. Periodic Motion is anything which repeats on a regular cycle. This can include large scale motion such as rotation and orbit of the Earth. It can also include the fluctuations of an electromagnetic wave!!. This can include Mass on a Spring!!.
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Vibrations and Waves They are All Around!!!
Periodic Motion is anything which repeats on a regular cycle.
This can include large scale motion such as rotation and orbit of the Earth.
It can also include the fluctuations of an electromagnetic wave!!
This can include Mass on a Spring!! • Simple Harmonic Motion is when the net force on a system is zero. • The force which pulls the mass out of position is equal to the force which restores the mass to its original position.
This can include Mass on a Spring!! • The time it takes for the system to complete one complete cycle of motion is the period (T). • The maximum distance the object moves from its equilibrium is the amplitude.
Hooke’s Law F = -kx • The force exerted by a spring is equal to how far the spring is stretched times the spring constant. • xis the distance stretched. • kis the spring constant which refers to stiffness and other factors.
Potential Energy • Not all springs obey Hooke’s Law but those that do are known as elastic springs. • Springs also have potential energy (measured in joules) • PEsp = ½ kx2
Pendulum Motion • Pendulum Motion is the motion of a string holding a bob moving back and forth. • The force of tension on the string and the force of gravity combine in vector addition to make a very predictable period of motion. • For hundreds of years clocks were made on this principle.
Pendulum Motion • For angles of 15° or less the restoring force is proportional to displacement, resulting in simple harmonic motion. • The only two factors which impact the period of the pendulum is the length of the string and the force of gravity, provided the bob creates enough tension.
Period of a Pendulum l T = 2 π g T = period of pendulum l = length of string g = gravity
Resonance Tacoma Narrows Bridge Collapse "Gallopin' Gertie" - YouTube • The application of force at intervals equal to the oscillation (frequency) can cause resonance, which leads to greater displacement.
Resonance • Resonance can also occur with sound and is the basic principal behind many musical instruments. • This is especially true of string and wind instruments.
Mechanical Waves • These waves move through a rope, string, water, air, or even solid objects. They require a medium. • They can be transverse or longitudinal. • Surface waves have characteristics of both transverse and longitudinal waves. • A wave pulse is a single disturbance and a periodic wave is a rhythmic disturbance.
Frequency • Frequency (f) is how many waves (complete oscillations) occur in 1 second. • It is measured in hertz (Hz). 1 f = T
Wavelength • Wavelength (λ) can be found by dividing wave speed by frequency. • It is measured in meters (m). v λ = f
Waves at Boundaries • The wave that strikes a surface is the incident wave. • The wave that bounces off a surface is the reflected wave.
Waves that hit a loose end or frictionless loop remain upright.
Waves that hit a more dense medium the reflected wave is inverted.
Waves that hit a less dense medium the reflected wave remains upright.
Standing Waves • Standing Waves are fixed at both ends, like guitar and violin strings. • Nodes are parts of the wave which do not move. • Antinodes have the greatest displacement.
