Periodic Motion and Energy Transfer

Periodic Motion When something is displaced from equilibrium position… AND experiences a restoring force… It is forced to oscillate “periodically”

Pendulum A pendulum can be pushed away from equilibrium A component of the gravitational force acts as the restoring force Simple Pendulum

Mass on a Spring Spring force is a restoring force When a mass stretches a spring from equilibrium, the restoring force causes oscillations Harmonic Oscillator Spring Pendulum

From Oscillations to Waves

What Is A Wave? A disturbance which causes energy to be transported from one location to another, without a transfer of mass. A form of periodic motion There are two different classifications of waves: Mechanical Waves Electromagnetic Waves (EM)

Mechanical Waves Waves are produced by a disturbance in a physical medium. The MEDIUM is the material through which the waves travel. The medium moves or oscillates back and forth, which causes energy to be transported from one location to another. Examples of mechanical waves include ocean waves, sound waves, and earthquake waves. What would be the mediums for these waves?

Electromagnetic (EM) Waves EM waves are created by oscillating electric and magnetic fields. EM waves require no medium to travel through. EM waves include such things as Light, X-Rays, Ultraviolet, Radio waves, and Infrared. We’ll discuss EM Waves in more detail later.

Three Types of Waves Transverse Waves- The particles of the medium move perpendicular to the wave motion. Longitudinal Waves- The particles of the medium move parallel to (along the direction of) the wave motion. Surface Waves- The particles of the medium move both parallel and perpendicular to the wave motion. vemotion.html vemotion.html

Transverse Waves

Longitudinal Waves

Surface Waves Surface waves occur at the surface of water or other materials. The particles of the medium travel in a circular fashion, which is a combination of transverse and longitudinal. Motion of Wave

Wave Pulse A wave pulse occurs if a single disturbance travels along a medium. Take a rope or spring, and give a quick jerk to one side, and then return it, you will create a wave pulse!

Traveling Waves If you create a wave pulse continuously, you will get a traveling wave. The source of the disturbance vibrates, causing a steady stream of wave pulses. This is called a traveling wave.

Wave Properties Period (T)- the time required for one complete wave to pass by a position. Frequency (f)- the number of waves that pass by per second. Wavelength (λ)- The ‘length of a wave’ is found by finding the distance between two successive identical points on a wave (i.e., from crest to crest or trough to trough) Amplitude (A)- The maximum displacement of the medium from the rest position.

Finding the Period of a Wave Suppose 12 waves pass by in 30 seconds. What is the period of these waves? T = time for one complete wave Time = 30 seconds for 12 waves T = (30 seconds) ÷ (12 waves) T = 2.5 seconds

Finding Frequency of a Wave Suppose 12 waves pass by in 30 seconds. What is the frequency of these waves? f = # of waves per second f = (12 waves) ÷ (30 sec.) f = 0.4 waves per sec This unit is called a Hertz (Hz) f = 0.4 Hz

Period and Frequency Notice that Period = time ÷ waves, and Frequency = waves ÷ time. So these two quantities are closely related. T = 1/f f = 1/T

Finding the Wavelength and Amplitude

Finding the Wave Speed Waves usually travel at a constant speed, so we can use d=vt, or v=d/t. The distance across a wave is the Wavelength (λ). The time it takes for one wavelength to pass is the Period (T). So, v=d/t becomes v=λ/T. Since T=1/f, then v=λ/1/f, or simply, v = λ f.

Wave Speed Example A sound wave with a frequency of 262 Hz has a wavelength of 1.29 m. What is the wave speed? V = f λ V = (262 Hz)(1.29 m) V = 338 m/s

Mechanical Waves Review Symbols and Units: Wavelength: λ (lambda) measured in m Frequency: f measured in Hz (1/s) Period: T measured in s Wave speed: v measured in m/s Amplitude: A measured in m Equations: T=time/wave and f=# waves/time T=1/f and f=1/T v= λ/T OR v= λf