AP PHYSICS B CHAPTER 13 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 pendulums Simple 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 Hooke’s law type of force Examples: springs

Definitions Amplitude – maximum displacement of an object from it’s 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 Law` Hooke's law is a principle of physics that states that the force needed to extend or compress a spring by some distance is proportional to that distance. That is: where is a constant factor characteristic of the spring, its stiffness. Hooke's law: the force is proportional to the extension.

Equations that are associated with Hooke’s Law

Elastic Potential Energy

Motion of a Pendulum A simple pendulum is another mechanical system that exhibits periodic motion Ft= -mgsin. Ф

Finding Period 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

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

Dissecting a Wave crest (peak) l A trough l Link to ISVR

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

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

Reflection of Wave Fronts 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.

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

Standing Waves 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.

Resonant Frequencies L Node Anti-node Link to ISVR

Sample Problem 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 cm A) 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 position B. ) What speed does the stone leave the slingshot. q

Sample Problem 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.