HOW DO WE DESCRIBE SIMPLE HARMONIC MOTION?

Why learn about waves? Waves carry useful

information and energy.

Waves are all around us: light from the stoplight ripples in a puddle of electricity flowing in wires radio and television and

cell phone transmissions

Characteristics of waves

Waves have cycles, frequency, and amplitude, just like oscillations.

The frequency of a wave tells how often each point oscillates.

The amplitude of a wave is the maximum movement from equilibrium.

The wavelength of a wave is the length of one complete cycle.

Periodic Motion

A motion of an object that repeats with a constant period.

http://www.sccs.swarthmore.edu/users/08/ajb/e71/lab1/

Simple Harmonic Motion

It is a periodic motion. AND

It has a restoring force that acts to restore the oscillator to equilibrium. The restoring force is given by:

Hooke’s Law F=-kxx is the displacement from equilibrium and k is the force constant (spring constant).

Describing Waves A vibration of a system in which some particular points remain fixed

while others between them vibrate with the maximum amplitude. Standing waves have nodes and antinodes. A node is a point where the string stays at its equilibrium position. An antinode is a point where the wave is as far as it gets from

equilibrium.

Guitar string & standing wave

http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/sound/soundtoc.html

Why Things Oscillate

Systems that have harmonic motion move back and forth around a central or equilibrium position.

Equilibrium is maintained by restoring forces.

A restoring force is any force that always acts to pull the system back toward equilibrium.

Harmonic Motion is Common

sound communications

clocks

nature

Position VS. Time graph

Amplitude

•Amplitude is the magnitude of the maximum displacement.

• For any object in simple harmonic motion, the time required to complete one cycle is the period T.

Frequency, f

The frequency f of the simple harmonic motion is the number of cycles of the motion per second.

Measured in Hertz (1/s) Hz

f = 1/T

Inertia

Newton’s first law explains why harmonic motion happens for moving objects.

According to the first law, an object in motion stays in motion unless acted upon by a force.

Relationship between speed, frequency, and wavelength

The speed of a wave equals the frequency times the wavelength.

v = f λFrequency (cycles/sec)

Wavelength (m)

Speed (m/sec)

What does the period depend on?

glT 2

Length of the pendulum (l).

Acceleration due to gravity (g).

Period does not depend upon the bob mass or the amplitude of the swing. Vibration of a pendulum.

The to-and-fro vibratory motion is also called oscillatory motion (or oscillation).

Transverse and Longitudinal Waves

A transverse wave has its oscillations perpendicular to the direction the wave moves.

A longitudinal wave has oscillations in the same direction as the wave moves.

Interference If two waves add up to create a larger amplitude,

constructive interference has occurred. In destructive interference, waves add up to make

a smaller amplitude.

Natural Frequency and Resonance

Waves can show natural frequency and resonance, just like oscillators.

The natural frequency of a wave depends on the wave and also on the system that contains the wave.

Resonance in waves is caused by reflections from the boundaries of a system.

How is a Sonic Boom created?

What Makes a Light Wave Different than a Sound Wave?

• Light travels a million times faster than sound:

Speed of light in air = 300,000,000 meters per second

• Speed of sound in air (at 0 Celsius) = 331 meters per second.

• Light can travel in empty space …Sound can’t because sound is the

compression of the medium

Transverse vs. Longitudinal Light is a transverse wave:Transverse means that the wave travels perpendicular to the

displacement

Sound is a longitudinal wave The wave travels in the same direction as the displacement

Light gets slower in denser objects (Faster: air, water, glass :Slower) Sound gets faster in denser objects (Slower: gas, liquid, solid :Faster)

Doppler Effect The Doppler effect can be described as

the effect produced by a moving source of waves in which there is an apparent upward shift in frequency for the observer and the source are approaching and an apparent downward shift in frequency when the observer and the source is receding.

http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/sound/soundtoc.html

http://cse.ssl.berkeley.edu/bmendez/ay10/2002/notes/pics/bt2lf0615_a.jpg

What is the Electromagnetic Spectrum?