# UNIT 5: VIBRATIONS, WAVES & SOUND

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UNIT 5: VIBRATIONS, WAVES & SOUND

SIMPLE HARMONIC MOTION
Position vs. time graph for an object shows how oscillations can create waves.

UNIT 5: VIBRATIONS, WAVES & SOUND
PHYSICS UNIT 5: VIBRATIONS, WAVES & SOUND

WAVES Energy transfer can occur by doing work, by heat, or by waves!
Wave: a disturbance (vibration) that travels mechanical waves require a material medium (solid, liquid, or gas) – particles vibrate in simple harmonic motion (water, sound, earthquake waves) electromagnetic waves travel through a material or a vacuum – vibrating electric and magnetic fields (radio, microwave, infrared, visible light, ultraviolet, x-ray, gamma rays)

WAVES Transverse waves: vibrations are perpendicular to wave direction

WAVES Longitudinal waves: vibrations parallel to wave direction
rarefaction

WAVES Frequency, f: number of waves each second, unit: Hertz (Hz) Hz = 1 wave/sec Period, T: time between identical points on two waves, unit: s f=1/T Wavelength, l: distance between identical points on two waves, unit: m

WAVES Amplitude, A: maximum displacement from equilibrium, unit: m
Wave speed, v: speed of the wave, not the particles, unit: m/s v=fl use difference in wave speeds to find distance ex: lightning & thunder

WAVES What could affect wave speed of a string being held tight between two points? Wave speed is also proportional to tension and inversely proportional to μ (mass per unit length m/L)

UNIT 5: VIBRATIONS, WAVES & SOUND
PHYSICS UNIT 5: VIBRATIONS, WAVES & SOUND

WAVE INTERACTIONS Each point on a wave travels in straight lines perpendicular to the wave front

WAVE INTERACTIONS Reflection: waves "bounce back" at boundary

WAVE INTERACTIONS Law of Reflection: qi = qr i: incidence, r: reflection

WAVE INTERACTIONS Reflection: with an open boundary
reflection is right-side-up

WAVE INTERACTIONS Reflection with a confined boundary
reflection is upside-down.

WAVE INTERACTIONS Absorption: wave energy becomes heat
Transmission: wave enters new medium, speed & l change

WAVE INTERACTIONS Interference: waves pass through each other without changing each other, but their displacements add together

WAVE INTERACTIONS constructive interference: combined wave displacement is greater than individual waves

WAVE INTERACTIONS destructive interference: combined wave displacement is less than individual waves

Interference Condition for constructive interference:
D1 – D2 = n l where n = 1, 2, 3… Condition for destructive interference: D1 – D2 = (n+1/2) l where n = 0,1, 2, 3… D1 is distance from first source to point D2 is distance from second source to point

WAVE INTERACTIONS Refraction: wave path bends as wave crosses boundary. Note that speed & wavelength change as wave moves into new medium, but frequency remains constant.

WAVE INTERACTIONS Refraction: wave bends toward the normal when it slows down

WAVE INTERACTIONS Refraction: wave bends away from the normal when it speeds up

WAVE INTERACTIONS Diffraction wave spreads out or “bends” beyond edge of barrier

WAVE INTERACTIONS Diffraction greatest when l is greater than or equal to the size of opening or object

WAVE INTERACTIONS Standing Waves: interference of two identical waves going opposite directions makes waves appear to vibrate in place

WAVE INTERACTIONS Standing Waves: nodes: no displacement
loops or antinodes: maximum displacement node distance = l/2

SOUND WAVES Source: a vibrating object (vocal cord, string, reed, etc.)

SOUND WAVES Wave type: mechanical longitudinal graph as transverse

SOUND WAVES Pitch: musical tone or note – frequency of a wave
sonic spectrum: musical scale: specific proportional frequencies C major scale C D E F G A B frequency (Hz) 264 297 330 352 396 440 495 528

MUSICAL INSTRUMENTS Stringed Instruments
string pitch = resonant vibrating frequency of string fundamental (lowest f): string is a single loop standing wave harmonic: integer multiple of fundamental

MUSICAL INSTRUMENTS l=2L/n L: length of string, and n is 1,2,3…
f=v/l v: wave speed in string v=√TL/m T: tension, m: mass of string

MUSICAL INSTRUMENTS Stringed Instruments
quality: mixture of fundamental and harmonics (makes different instruments sound different) sound boards & boxes: more air surface contact - amplifiers

MUSICAL INSTRUMENTS

MUSICAL INSTRUMENTS Wind Instruments
pitch = frequency of vibration of column of air f = v/l v: sound speed in air l: wavelength, depends on length of air column

MUSICAL INSTRUMENTS open-end tube: each end of tube is antinode
l = 2L/n L: length of tube and n is 1,2,3… Examples: flutes, saxophones, some organ pipes

MUSICAL INSTRUMENTS closed-end tube: closed end of tube is node
l=4L/n L: length of tube and n is 1,3,5 Examples: clarinets, some pipe organs

UNIT 5: VIBRATIONS, WAVES & SOUND
PHYSICS UNIT 5: VIBRATIONS, WAVES & SOUND

SOUND INTERACTIONS Echo: sound wave reflection; maximum from rigid, smooth surfaces sonar: distance by timing pulse echoes, x = vsoundt (repeated echoes give a "picture" of surface) ultrasound: sonar using 1-10 MHz waves (detects smaller objects, inaudible); body vsound = 1540 m/s

SOUND INTERACTIONS Resonance (sympathetic vibration)
objects have natural vibrating frequency sending waves to an object at at its natural frequency will make it vibrate pushing a child on a swing using microwaves to heat up water

SOUND INTERACTIONS

SOUND INTERACTIONS The Doppler Effect: apparent change in frequency due to motion of source or listener

SOUND INTERACTIONS The Doppler Effect Source is moving toward observer
Observer is moving toward the source Vs = speed of source fo = observed frequency fs = frequency of source V0 = speed of observer C = wave speed

SOUND INTERACTIONS The Doppler Effect
Source is moving away Vs = speed of source fo = observed frequency fs = frequency of source V0 = speed of observer C = wave speed Observer moving away from the source

Doppler Effect What if both source and observer are moving?
If observer and source are moving toward each other then (+/-) If observer and source are moving away from each other then (-/+) Vs = speed of source fo = observed frequency fs = frequency of source V0 = speed of observer C = wave speed

SOUND INTERACTIONS Radar: uses Doppler Effect in radio waves reflected off an object to determine its speed Red shift and Blue shift of light tells astronomers whether a star is moving toward or away from Earth.

SOUND INTERACTIONS

SOUND INTERACTIONS The Doppler Effect
sound barrier: “pile-up” of sound waves (pressure) in front of object traveling Mach 1 sonic boom: cone-shaped pressure pulse following an object traveling at supersonic speeds (water wake following a speedboat)

SOUND INTERACTIONS

UNIT 5: VIBRATIONS, WAVES & SOUND
PHYSICS UNIT 5: VIBRATIONS, WAVES & SOUND

QUIZ 5.4 The speed of sound in earth is 3500 m/s. An earthquake wave, frequency 5 Hz, travels from its source to a distant mountain range and returns in 3.4 minutes. (a) How far away is the mountain range? (b) What is the wavelength of the earthquake wave? (c) If the mountain range was moving away at 0.50 m/s. what would be the frequency of the reflected wave? 357,000 m 700 m 5.00 Hz

UNIT 5 REVIEW f = 1/T v = fl qi = qr visinqr = vrsinqi node dist = l/2
loop height = 4A v = T I = P/4pr2 b = 10log(I/I0) I0 = 1× 10-12 W/m2 open pipe l = 2L closed pipe l = 4L x = vt