Chapter 11

Chapter 11

Conditions:
The net force on an object needs to be directly proportional to the objects vector displacement from its equilibrium position and oppositely directed.

Net force is proportional to negative displacement from equilibrium.

Force, Velocity, and Acceleration during Simple Harmonic Motion
Velocity: In simple harmonic motion, the velocity constantly changes, oscillating just as the displacement does. When the displacement is maximum, however, the velocity is zero; when the displacement is zero, the velocity is maximum.

Acceleration: The acceleration also oscillates in simple harmonic motion. If you consider a mass on a spring, when the displacement is zero the acceleration is also zero, because the spring applies no force. When the displacement is maximum, the acceleration is maximum, because the spring applies maximum force; the force applied by the spring is in the opposite direction as the displacement.

Force: The force acting on the wave must vary in the same way that the acceleration varies since F=m*a.

Calculate the force using Hookes Law
Hooke's Law: F=kx

Ex: When a 13.2-kg mass is placed on top of a vertical spring, the spring compresses 5.93 cm. Find the force constant of the spring.

From Hooke's Law: F = kx The force on the spring is the weight of the object, 13.2*9.8 = 129 N x = 5.93 cm =0.0593 m 129 = (0.0593)x x = 2181 N/m More problems with answers:http://www.physics247.com/physics-homework-help/elastic-potential.php

Amplitude of Vibration

Relationships: period and frequency
They are inverses!p^-1=f; f^-1=p

Calculating Period and Frequency:
Period: T=1/fFrequency: f=1/T

How particles move in a wave:
Longitudinal Waves: Particles simply oscillate back and forth over their equilibrium position. Ex: P wavesTransverse Waves: Particle displacement it perpendicular to the direction of wave propagation. Ex: S waves

Pulse Waves and longitudinal waves waveforms:
Pulse waves: A pulse wave is a type of non-sinusoidal waveform.

Longitudinal waves: Longitudinal waves, also known as "l-waves", are waves in which the displacement of the medium is in the same direction as, or the opposite direction to, the direction of travel of the wave.

Wave speed, frequency, and wavelength relationships in use:
Ex: A sound wave has a frequency of 3250 Hz and a wavelength of 0.1, what is its velocity? Answer: Use v = f * v = 3250 * 01= 325 m/s.

More examples on: http://www.gcsescience.com/pwav6.htm

Relate Energy and Amplitude:
Amplitude^2=powerPower*time=energy

Superposition Principle:
When two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location.

Constructive/Destructive Interference
Constructive: Adding two waves point by point, the resultant will be larger than the two original.

Destructive: The sum of the waves equals zero.http://www.physicsclassroom.com/class/waves/Lesson-3/Interference-of-Waves

Inversion of Reflected Wave:
Waves bounce off of a fixed point which inverts the reflectedwave.

Production of Standing Waves:
Standing waves are created when the medium is vibrated at a specific frequency, a harmonic. Specific points appear to be "standing still".

http://www.physicsclassroom.com/class/waves/Lesson-4/Formation-of-Standing-Waves

Nodes and Antinodes
Node: Point along the wave where amp. is minimum.

Antinode:Maximumamplitude