Waves

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# Waves - PowerPoint PPT Presentation

Waves. the transfer of energy without the transfer of matter. A Simple Look at a Wave. How many wavelengths in the wave below?. crest. amplitude. A. wavelength. λ. trough. how many λ pass per second. frequency =. units: per second. time for 1 λ to pass by. period=. or.

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Presentation Transcript
Waves

the transfer of energy without the transfer of matter

A Simple Look at a Wave
• How many wavelengths in the wave below?

crest

amplitude

A

wavelength

λ

trough

Ex.The wave below takes 10 seconds to pass by.

What is the period?

What is the frequency?

Types of Waves

Transverse wave:

medium vibrates at right angles to the direction the energy moves

λ

Compression wave:

(longitudinal wave)

medium vibrates in the same direction as the direction the energy moves

Electromagnetic Waves
• Mechanical waves require a mediumin order to travel.
• examples:
• electromagnetic waves do not require a medium

water,

earthquakes,

and sound

Electromagnetic Waves

All EM waves travel at 3.0 x 108m/s

Electromagnetic Waves

Radio waves are the longest of the spectrum

Electromagnetic Waves

Visible light is a tiny section

Electromagnetic Waves

Visible light is betweenultraviolet (UV) light and Infrared (IR) light

v

v

Interference
• Superposition: when two or more waves overlap
• Waves do not affect each others identity
Interference
• overall amplitude is sum of individual wave amplitudes
• Interference Example
Practice

Each wave pulse moves 1 grid at a time

Practice

Each wave pulse moves 1 grid at a time

Practice

sketch where wave would be if alone

Practice
• Waves above rest are positive
• below are negative
Practice

+2

0

Practice

+2

+2

0

Practice

0

+2

-2

Practice

0

+2

-2

Practice

-2

0

-2

Practice
• Move another grid and repeat process
• (remember, if both same sign then they stack/add)
• Now try it yourself
SOUND
• Sound is a compressionalwave
• Speed of sound depends on the medium
• fastest in solids (6000 m/s in steel)
• slower in liquids (1500 m/s in water)
• slowest in gases
Speed of sound in Air

speed of sound at 0 °C

At average temperature:

20 °C

If no temperature is given in a problem, assume 20° C (343 m/s)

Distance
• If you hear lightning 3.0 seconds after seeing it, how far away did it strike?
Characterizing Sound
• Sounds waves are characterized by their:
• speed
• pitch
• loudness
• quality
Pitch
• Pitch depends on frequency
• Young healthy human ear has a range of 20 Hz to 20,000 Hz
• Human voice: 120 Hz to 1,100 Hz
• Baby cry: 2,000 – 3,000 Hz
Octaves
• The octave is important in music
• Octave is the doubling in ƒ
• Ear can hear a range of ≈ 10 octaves
• 20 Hz  40 Hz  80 Hz 

160 Hz 

320 Hz 

640 Hz 

1280 Hz 

2560 Hz 

5120 Hz 

10,240 Hz 

20,480 Hz

Just Noticeable Difference (JND)
• The range that the ear can distinguish tones (pitches)
• at <1000 Hz, JND ≈ 1Hz
• this means you can tell the difference between 500 Hz and 501 Hz
• at 2,000 Hz, JND ≈ 2 Hz
• at 4,000 Hz, JND ≈ 10 Hz
• Test it
Loudness of Sound
• depends on amplitude of a sound wave
• new unit decibel (db)
• decibel is based on human hearing
• 0 decibels is the threshold of hearing
• 140 db is the sound of a jet on runway
Loudness of Sound
• decibel scale is logarithmic
• So, 60 db  70 db means 10x louder
• 60 db  80 db means 100x louder
• 140 db is 100,000,000,000,000x louder than 0 db
Decibel Details
• Sound Intensity Level (L) = db
• measures how loud you perceive sound
• Sound Intensity (I) = W/m2
• measures physical intensity of sound
• threshold I = 1 x 10-12 W/m2
Decibel Details
• threshold = 0 db = 1 x 10-12 W/m2
• I2 = heard sound
• I1 = sound you compare to
• (usually 1x 10-12 W/m2)
Example
• How many decibels would sound have if it had an intensity of 1 x 10-10 W/m2?
• given:

for normal problems, use 1 x 10-12 W/m2 for I1

Example
• What is the sound Intensity of a girl yelling at 86 db?

but this time, we want I2

Power!

Energy rate produced by a sound

units are Watts (W)

Power!

Power depends only on source, not distance

• this can be used to find I at different distances
Power Example:

What is the power of a jet engine when standing 5.0 m away from it?

given:

r = 5.0 m

L = 140 db

need I first

Frequency Sensitivity

The ear is much more sensitive to some pitches than others. How much more sensitive are we to a crying baby (3,000 Hz) than to normal talking (1,000 Hz)?

### Practice

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Doppler Effect

Pig standing still

OINK!

λ in front

is same as λbehind

Doppler Effect

Pig running right

OINK!

λ in front

is smaller λthan behind

Who hears the higher pitch?

Calculating Doppler Effect
• Doppler Effect occurs if either source or listener is moving
• ƒ’ = frequency the observer hears
• ƒ = actual frequency of source
• ν = speed of sound (remember T)
• νo = speed of observer
• νs = speed of source
Picking Signs

Ex: On a day when the speed of sound is 350 m/s, a police car with a 2,000 Hz siren and a speed of 35 m/s is chasing a car moving at 50. m/s. What frequency does the driver of the car hear?

• what is the source?

police car (it has the siren)

• what is the observer?

chased car

Given:

moving away from source

moving toward the observer

Picking Signs

Given:

So,

Now to pick signs. This requires logic.

Picking Signs

Numerator(observer)

If observer travels away from source, pitch goes down.

• for pitch to go down, vo must be negative

If observer travels towardsource, pitch goes up.

• for pitch to go up, vo must be positive
Picking Signs

Denominator(source)

If source travels away from observer, pitch goes down.

• for pitch to go down, vs must be positive

If source travels towardobserver, pitch goes up.

• for pitch to go up, vs must be negative
Put it together

observer moving away from source (-)

source moving towards observer (-)

car hears a lower pitch!

Do you get it?

Ex: It’s 33°C and you’re moving at 45m/s on a head-on collision course with another car moving at 35m/s. You lean on your 1,800Hz horn. What frequency does the other driver hear?

Given:

moving toward the source

moving toward the observer

Do you get it?

Given:

Find the speed (T = 33°C)

Do you get it?

Given:

Now let’s choose signs

moving toward the source

moving toward the observer

Pitch goes up!

Faster than the Speed of Sound
• Objects moving faster than sound make shock waves from the pushed air and sound.
• An observer would hear this as a crack!
• See the sounds waves
Faster than the Speed of Sound

Which plane is moving faster?

Mach 6

Mach 3.5

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