UNIT 5: VIBRATIONS, WAVES & SOUND

SIMPLE HARMONIC MOTION

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

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) 1 Hz = 1 wave/sec Period, T: time between identical points on

two waves, unit: s f=1/T Wavelength, : 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=f 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)

T

v

PHYSICS

UNIT 5: VIBRATIONS, WAVES & SOUND

WAVE INTERACTIONS Each point

on a wave travels in straight lines perpendicular to the wave front

WAVE INTERACTIONS Reflectio

n: waves "bounce back" at boundary

WAVE INTERACTIONS Law of Reflection: i = r i: incidence, r:

reflection

WAVE INTERACTIONS Reflectio

n: 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 & 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 where n = 1, 2, 3…

Condition for destructive interference:D1 – D2 = (n+1/2) 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 Refractio

n: wave bends toward the normal when it slows down

WAVE INTERACTIONS Refractio

n: wave bends away from the normal when it speeds up

WAVE INTERACTIONS Diffractio

n wave spreads out or “bends” beyond edge of barrier

WAVE INTERACTIONS Diffraction

greatest when is greater than or equal to the size of opening or object

WAVE INTERACTIONS Standing

Waves: interference of two identical waves goingopposite directions makes waves appear to vibrate in place

WAVE INTERACTIONS Standing

Waves: nodes: no

displacement loops or

antinodes: maximum displacement

node distance = /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:

C major scale C D E F G A B C

frequency (Hz)

264

297

330

352

396

440

495

528

musical scale: specific proportional frequencies

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 =2L/n

L: length of string, and n is 1,2,3…

f=v/v: wave speed in string

v=√TL/mT: 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/v: sound speed in air : wavelength, depends on length of air column

MUSICAL INSTRUMENTS open-end tube: each end of tube is

antinode = 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 =4L/n L: length of tube and n is

1,3,5 Examples: clarinets, some pipe

organs

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

C

Vf

fs

so

1

Vs = speed of sourcefo = observed frequencyfs = frequency of sourceV0 = speed of observerC = wave speed

Observer is moving toward the source

C

Vff oso 1

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

CVf

fs

so

1

C

Vff oso 1

Observer moving away from the source

Doppler Effect

Vs = speed of source fo = observed

frequency fs = frequency of source V0 = speed of observer C = wave speed

If observer and source are moving toward each other then (+/-)

If observer and source are moving away from each other then (-/+)

s

oso VC

VCff

What if both source and observer are moving?

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

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 = f i = r

visinr =

vrsini

node dist = /2

loop height = 4A

v = 331 + 0.6T

I = P/4r2

= 10log(I/

I0)

I0 = 1×

10-12 W/m2

open pipe = 2L

closed pipe = 4L

x = vt

km

2Ts gL

2Tp

B

v

E

vmTL

v

S

Lsh vv

vvff

S

Lsh vv

vvff