Wave Properties

Types of Waves Mechanical waves Water waves, sound waves, waves that travel along a spring or rope Requires a material medium Newton’s laws govern the motion of mechanical waves

Types of Waves Electromagnetic waves Light waves, radio waves, X-rays No medium is needed All travel through space at the speed of light 2.99 x 108m/s Details cannot be observed directly Will use the easily observed mechanical waves as models for the behavior of EM waves

Types of Waves Matter waves Electrons and other particles show the wave-like behavior under certain conditions Quantum mechanics are needed to describe these properties

Mechanical Waves Three different types Each type disturbs the media in a different way Transverse wave Longitudinal wave Surface wave

Transverse Wave Causes the medium to vibrate perpendicularly to the direction of motion of the wave Example: waves in piano and guitar strings

Longitudinal Wave Causes the particles of a medium to move parallel to the direction of the wave Example: sound wave Fluids, liquids, gases, or plasma usually only longitudinal

Surface Wave Mixture of transverse and longitudinal waves Energy of water waves usually comes from storms far away

How are waves produced? Wave pulse: single disturbance that travels through a medium A given point was at rest before the pulse reached it; it returned to rest after the pulse passed Created by sudden jerking of the rope to one side and returning to center Traveling wave Created by moving rope side to side in a regular manner A source that is vibrating with simple harmonic motion will produce a continuous travelling wave

Measures of a Wave Period (T): shortest time interval over which the motion repeats itself Frequency (f): number of complete vibrations/sec; measure at a fixed location Measured in Hertz (Hz) 1 Hz = 1 vibration/sec F = 1/T

Example Problem p291 A sound wave has a frequency of 262 Hz. What is the time between successive wave crests? Given: f = 262 Hz

Example Problem p291 A sound wave has a frequency of 262 Hz. What is the time between successive wave crests? Given: f = 262 Hz T=?

Example Problem p291 A sound wave has a frequency of 262 Hz. What is the time between successive wave crests? Given: f = 262 Hz T=? F = 1/T

Example Problem p291 A sound wave has a frequency of 262 Hz. What is the time between successive wave crests? Given: f = 262 Hz T=? f = 1/T 262 = 1/T T = 1/262 T = 3.82 x 10-3 s

Measures of a Wave Wavelength: shortest distance between points where the wave pattern repeats itself Represented by λ Crests: high points of each wave Troughs: low points of each wave Each crest is one wavelength from the next crest; troughs are also spaced by one wavelength V = λ / T or v = λf

Measures of a Wave Amplitude Two waves with the same frequency can have different λ Amplitude: maximum displacement from rest or equilibrium position Example: rope shaken gently vs. violently; sound loud vs. soft; water wave giant tidal vs. ripple To produce a wave with greater amplitude more work has to be done Example: strong winds produce larger water waves than gentle breezes A wave with larger amplitude transfers more energy Double the amplitude then you increase the energy it transfers every second by a factor of 4

Example Problem p293 A sound wave with frequency of 262 Hz has a wavelength of 1.29 m. What is the velocity of the sound wave?

Example Problem p293 A sound wave with frequency of 262 Hz has a wavelength of 1.29 m. What is the velocity of the sound wave? Given: f = 262 Hz λ = 1.29 m

Example Problem p293 A sound wave with frequency of 262 Hz has a wavelength of 1.29 m. What is the velocity of the sound wave? Given: f = 262 Hz λ = 1.29 m v = ?

Example Problem p293 A sound wave with frequency of 262 Hz has a wavelength of 1.29 m. What is the velocity of the sound wave? Given: f = 262 Hz λ = 1.29 m v = ? v = λf

Example Problem p293 A sound wave with frequency of 262 Hz has a wavelength of 1.29 m. What is the velocity of the sound wave? Given: f = 262 Hz λ = 1.29 m v = ? v = λf v = λf v = (1.29)(262)

Example Problem p293 A sound wave with frequency of 262 Hz has a wavelength of 1.29 m. What is the velocity of the sound wave? Given: f = 262 Hz λ = 1.29 m v = ? v = λf v = λf v = (1.29)(262) v = 338 m/s