Waves

Physics - Definitions, Properties, and Calculations

Wave Definitions• Transverse Waves - Vibrations of a transverse wave are

perpendicular to the wave motion• Longitudinal Waves - the displacement of the medium is

parallel to the propagation of the wave • Simple Harmonic Motion - periodic motion in which the

restoring force is proportional to the displacement • Crest – Top of the wave motion• Trough – Bottom of the wave motion• Amplitude – How high the pendulum goes or begins with.• Period – The time it takes to make one complete

revolution.• Wavelength – The distance from crest to crest or trough to

trough• Frequency=the number of crests or troughs that pass a

given point in a unit of time. - 1/period. Measured in Hertz or hz.

Waves Types

• Waves that require a material medium are called mechanical waves. (sound waves, water waves etc.)

• Electromagnetic waves, such as visible light, radio waves, microwaves, and X rays, can travel through a vacuum

Transverse Waves• Vibrations of a transverse wave are perpendicular

to the wave motion• Examples: Water waves, rope waves, EM waves• Pulse wave: A rectangular wave created by a

pulse of energy.• Sine Wave: mathematical curve that describes a

smooth repetitive oscillation

Transverse Activity

1. Put a piece of tape in about the middle of the rope.2. Tie your rope to something or let your friend hold on

to one end of it.3. Now pull the rope so that it is a bit slack but not quite

touching the floor.4. Vibrate your arm. Move your arm up and down once

and watch what happens.5. Now, vibrate your arm a bunch of times (not too fast)

and see the results. Notice the action of the tape in the middle of the rope.

Click to Run

Longitudinal Wave

• Vibrations of a longitudinal wave are parallel to the wave motion

• When the particles of the medium vibrate parallel to the direction of wave motion

• Sound waves in the air are longitudinal waves

Longitudinal Activity

• 1. Put a piece of tape on one slinky wire in the middle or so of the slinky.

• 2. Let your friend hold on to one end of the slinky or anchor the slinky to a chair or table.

• 3. Now stretch the slinky out, but not too far.• 4. Quickly push the slinky toward your friend, or the

table, and then pull it back to its original position. Did you see the wave?

• 5. Now do it again, back and forth several times and watch where the slinky is bunched up and where it's spread out.

• 6. Notice the tape. What is it doing?

Click to Run

Harmonic Motion and Wave Calculations PERIOD, FREQUENCY, AND WAVE SPEED

• Period – Represented by T. The period of a wave is the amount of time required for one complete vibration of the particles of the medium. In a pendulum it is the time to go right and then left.

• Frequency – Measured in HZ and represented by f. How many times a wavelength(lambda) moves in a give time period.

• Wave Speed – The velocity of the wave.

Wave Speed Questions

• 1. A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz. Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 m/s.

• 2. The speed of all electromagnetic waves in empty space is 3.00 x 108 m/s. Calculate the wavelength of electromagnetic waves emitted at the following frequencies:

• a. radio waves at 88.0 MHz • b. visible light at 6.0 x 108 MHz • c. Xrays at 3.0 x 1012MHz

Harmonic Motion of a Pendulum

• Bob – The weight of a pendulum

• String Length – How far the bob is from the pivot

• Formula:

http://en.wikipedia.org/wiki/File:Oscillating_pendulum.gif

Harmonic Motion Questions

• 1. If the period of the pendulum in the preceding sample problem were 24 s, how tall would the tower be?

• 2. You are designing a pendulum clock to have a period of 1.0 s. How long should the pendulum be?