Vibrations and Waves

Periodic Motion is said to occur when an object vibrates or oscillates over the same path again and again. Examples: springs and pendulumsSimple Harmonic Motion is a special form of periodic motion in which the restoring force is proportional to the displacement of the object. It occurs when the net force along the direction of the motion is a Hookes law type of force Examples: springs

Amplitude maximum displacement of an object from its equilibrium point. Cycle one complete to-and-fro motion. Period time required to complete one cycle. Frequency number of cycles completed each second. Recall:

Hooke's lawis a principle ofphysicsthat states that theforceneeded to extend or compress aspringby some distanceis proportional to that distance. That is:whereis a constant factor characteristic of the spring, itsstiffness.Hooke's law: the force is proportional to the extension.

A simple pendulum is another mechanical system that exhibits periodic motionFt= -mgsin

To find the period of an pendulum in SHM, you can simply use the following equation:To find the period of an ideal spring in SHM, you can simply use the following equation:

Equations of SHM

Mechanical Wave wave that travels through a medium. There are two types of mechanical waves. Transverse object particles move perpendicular to the waves motion. Longitudinal object particles move parallel to the waves motion. Link to: The Institute of Sound and Vibration Research.

crest (peak)troughDissecting a WaveLink to ISVR

Fixed PointWhen the wave strikes a fixed point, the wave becomes inverted. the wave remains erect. Free PointWhen the wave strikes a free point, Wave Reflection

When transmitting to a less dense material: When transmitting to a more dense material: Frequency remains the same. Velocity increases. Wavelength increases. Reflected wave is small. Transmitted wave is big. More of the wave will be reflected back along the lighter cord. Frequency still remains the same. Velocity and wavelength decrease. Wave Transmission

Two- or three-dimensional waves travel along wave fronts. The motion of these waves can be seen using rays drawn perpendicular to each wave front. Law of reflection angle of incidence equals angle of reflection.

Principle of Superposition when two waves overlap, the resultant displacement will be the algebraic sum of their separate displacements. Constructive Interference waves are in phaseDestructive Interference waves are out of phaseInterferenceLink to ISVR

Standing wave when reflected waves are in phase with incident waves and the wave appears to stand still. Fundamental Mode or Frequency frequency at which a standing wave of the lowest resonance can be produced. Resonant Frequencies frequencies at which standing waves are produced.

Link to ISVR

A mass of 4 kg can stretch a spring by 0.5 m. Determine the spring constant of the spring.

A slingshot consists of a light leather cup containing a stone that is pulled back against two rubber bands. It takes 30 N to stretch the bands 1.0 cmA) What is the potential energy stored in the bands when a 50 g stone is placed in the cup and pulled back 0.20 m from the equilibrium positionB.) What speed does the stone leave the slingshot.

A device used to test guitar strings hangs a mass off the end of a string, and then sends waves throughout the string at a rate of 120 Hertz (cycles/second) to determine if the string has the correct mass to length ratio. For a particular string, a mass is hung over a pulley that is 0.6 meters away, and hanging a mass of 4 kg creates a standing wave with 6 loops. Determine the m/L ratio of the string.

AP Physics B, WavesMarcopul-Pandya, 2006-2007*AP Physics B, WavesMarcopul-Pandya, 2006-2007*AP Physics B, WavesMarcopul-Pandya, 2006-2007*AP Physics B, WavesMarcopul-Pandya, 2006-2007*