Waves Chapter 25

Vibrations and Waves A wiggle in time is a vibration –A vibration cannot exist in one instant but needs time to move back and forth A wiggle in space and time is a wave –A wave cannot exist in one place but must extend from one place to another The source of all waves is something that vibrates

Methods of Energy Transfer Energy can be transferred by: movement through material (matter) or by waves Wave = disturbance that propagates through a medium or space (no matter) 2 types of waves: electromagnetic (travels through matter but does not need matter) or mechanical which requires matter

Electromagnetic Spectrum

Light, radio, TV or x-rays examples of EMG waves-most common type Can travel through a vacum Transverse waves-displacement of particles is perpendicular to the direction of the source

Transverse Waves The motion of the wave is at right angles to the direction in which the wave is moving. Whenever the motion of the medium is at right angles (perpendicular) to the direction in which the wave travels

Water, sound, waves on a rope = mechanical waves Define as a disturbance in the equilibrium position of matter Generate: source of energy causes a disturbance & an elastic medium moves parallel to the direction of the source==longitudinal waves

Longitudinal Waves The particles move along the direction in which the wave travels. Particles move back and forth in the same direction in which the wave travels

Single non-repeated disturbance = single crest (upward displacement) or single trough (downward displacement) called a single wave pulse or a pulse Periodic succession of positive & negative pulses = wave train or continuous wave

Parts of A Wave Crest – high point in the wave Trough – low point in the wave Amplitude – distance from the midpoint to the crest (or trough) of the wave. –Amplitude equals the maximum displacement Wavelength is the distance from the top of one crest to the top of the next one or the distance between identical parts of the wave

Parts of a wave Sine Curve

Wave Characteristics In phase = same displacement & move in same direction Out of phase = moving in opposite direction & in opposite phase Pulse-single disturbance [single crest or single trough] Wave or wave train-succession of crests or troughs

Wave Energy Energy is transmitted from 1 point to another. Energy is transferred & NOT matter. Energy depends on: amplitude, frequency and mass of particles of the medium Waves will transfer energy but not the matter within the medium

Measuring a Wave How often a vibration occurs is frequency –Specifies the number of back and forth vibrations something makes in a given time cycle –Unit of frequency is the hertz (Hz) –AM Radio is broadcast in kHz Kilohertz –FM Radio is broadcast in MHz Megahertz 1 cycle is 1 hertz, 2 cycles is 2 hertz and so on

Frequency Frequency – Frequency = 1 disturbance divided by 1 sec – Period is the time it takes for one cycle to occur; measured in seconds; distance from 1 crest to the next –Frequency and Period are inverse –f = 1/T or f = disturbance/ 1 sec –T = 1/f

Wave Speed The speed of a wave depends on the medium it’s traveling through Wave speed = wavelength x frequency – v = f ( ) – v = wave speed, f = frequency, and = (lambda) is wavelength Wavelength and frequency vary directly with each other: lots of wavelengths = high frequency

Simple Harmonic Motion Motion that repeats over and over is considered Harmonic Motion –Cycle: is the unit of motion that repeats over and over –A system that shows harmonic motion is an oscillator-example is pendulum –When the pendulum moves over a moving object it traces a sine curve also an example of transverse wave

Wave Interactions Properties of all waves: rectilinear (straight-line) motion; reflection, refraction, diffraction, & interference Ripple tank can be used to observe wave interactions Most characteristic of all wave properties is interference.

Reflection of Waves Reflection-when a wave is turned back when it encounters a barrier; Law of Reflection: angle of incident = angle of reflection Types of barriers or boundaries: rigid (more dense) or less rigid (less dense)

Pulse that reflects off a more dense media Moves from air into water or air into a mirror surface

Reflection of a pulse: Off of a less dense media Moves from air into air OR water into air

Reflection: less dense to more dense media

COPY THIS! More rigid barrier than original medium = pulse is partially reflected & is equal to the incident but travels inverted ** See example Less rigid barrier than original medium = cause total reflection & reflected pulse will be erect (in same original plane) **See example **See example Reflection depends on the medium

Refraction Refraction-bending of the path of a wave as it passes obliquely from 1 medium into another- SPEED CHANGES so “bends” the wave Wave passes into more dense medium = wave is bent toward the normal = wave has slowed down See example Wave passes into less dense medium = wave is bent away from the normal = wave has gained speed See example

Diffraction Diffraction-spreading of a wave beyond the edge of a barrier-spreading “around” the edges Common with sound and light energy

Interference Constructive Interference: –when the crest of one wave overlaps the crest of another wave individual effects add together—energy is increased –The result is a wave of increased amplitude ** See example Destructive Interference: –When the crest of one wave overlaps the trough of another, their individual effects are reduced ** See example –The high part of one wave simply fills in the low part of another—energy reduced

Constructive Interference

Destructive Interference

Standing Waves The incident (original) and reflected waves form a standing wave –In certain parts of the rope, called nodes remain stationary –The position on a standing wave with the largest amplitudes are know as antinodes Nodes & anti nodes are the result of interference

Standing Wave in Motion

Nodes-points of zero displacement in interference-”dead spots” Anti nodes-points of maximum displacement in interference Loops-1/2 way between nodes where amplitude is maximum

Standing wave

Doppler Effect/Bow Waves Doppler effect: change in frequency due to motion of the source or receiver; change in pitch See pg. 374 Doppler effect is also found in light energy called blue shift or red shift Bow waves: v-shaped wave produced by an object moving on a liquid surface faster than the wave speed pg. 375

Shock Waves Shock waves: cone-shaped wave produced by an object moving at supersonic speed through a fluid Sonic boom---the sharp crack heard when the shock wave sweeps behind a supersonic aircraft reaches the listener

PROBLEMS Frequency ( f ) = number of waves/ time; how often a vibration occurs Measured in units called: hertz (Hz) If a water wave vibrates up & down 2 times each second, what is the frequency? If 33 crests pass in 30 seconds in a wave front, what is the frequency?

PROBLEMS Period—is the time of wave movement Measured in seconds Period is the inverse of frequency Formula: T = 1/ f or f = 1/T What is the period of a water wave that is 6 cm long & passes a given point at the rate of 4.8 waves per second.

Two physics students were fishing. One student observed the boat rocked 11 complete oscillations in 19 sec & that one wave crest passed the boat each oscillation. What is the period of the surface wave?

WAVE SPEED Wave speed depends on frequency and wavelength Wave speed is measured in m/sec or km/hr If a distance of 2.5 m separates a trough & an adjacent crest of water waves on the surface of a lake, and 33 crest pass in 30 seconds. What is the speed of these waves?

A wave has a speed of 50 m/sec and a frequency of 10 Hz. Calculate its wavelength.

Key Terms AmplitudeAntinodes Constructive interference Crest Destructive interference FrequencyHertz Longitudinal Wave NodePeriod Simple harmonic motion Sine curve Standing wave Transverse wave TroughVibrationWaveWavelength

Animation courtesy of Dr. Dan Russell, Kettering University