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Chapter 6

WAVES

Dr. Babar Ali

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CHAPTER OUTLINE

Wave Concept Wave Properties Wave Speed Wave Types Electromagnetic

Waves

Sound Waves Speed of Sound Doppler Effect Standing Waves Resonance

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CONCEPT OF WAVES

A wave is a disturbance that propagates through a system transferring energy

Waves transfer E!

(courtesy of Dr. Dan Russell, Kettering Univ.)

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WAVE PROPERTIES

Crest: the highest point on a wave

Trough: the lowest point on a wave

Amplitude: maximum displacement in a wave

height of crest or depth of trough

Amplitude is related to the E

of a wave

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WAVE PROPERTIES

Wavelength (λ): distance between 2 successive crests

Frequency (f): # of waves produced per unit time.

Units = m or cm

Units = 1/s = Hz

Period (T): # of seconds per unit wave.

1f =

T

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WAVE SPEED

The speed of a wave can be calculated from its frequency (f) and wavelength (λ).

f × λ = s

Units:

Note, s = constantfor a given wave

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Example 1:

A sound wave has a speed of 344 m/s and a wave-length of 0.5 m. What is the frequency of this wave?

f = ???

λ = 0.5 m

s = 344 m/sf = 688 Hz

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Example 2:

sλ =

f

344 m/s=

20 x 1000 Hzf = 20 kHz

λ = ???

s = 344 m/s λ = 0.017 m

A sound wave has a speed of 344 m/s has a frequency of 20 kHz. What is this wave’s wavelength?

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Example 3:

An ocean wave passes a point on the pier at the rate of 12 waves per minute. What are the frequency and period of this wave?

# of cycles = 12

time = 60 s

f = ???

T = ???

f = 0.2 Hz

T = 5 s

12 waves=

60 s

1=

0.2 Hz

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LONGITUDINALWAVES

Waves where direction of particle movement is parallel to the direction of wave velocity, are longitudinal waves

Longitudinal waves have areas of high particle density (compressions) and of low particle density (rarefactions)

Sound is the most common example of a longitudinal wave.

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TRANSVERSEWAVES

Waves where the direction of particle movement is perpendicular to the direction of wave velocity, are transverse waves

i.e. mechanical waves, electromagnetic waves (light, microwave, x-rays, etc.)

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ELECTROMAGNETICWAVES

Electromagnetic waves (e&m waves) are transverse waves caused by vibrating electrons (e-) Formed through interaction of electric and magnetic fields that

are perpendicular to one another

In vacuum, e&m waves travel at the same speed and differ from each other only in freq.

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ELECTROMAGNETICSPECTRUM

The classification of electromagnetic waves according to their frequency is called electro-magnetic spectrum.

e&m waves range from γ rays (short λ , high f) to radio (long λ, low f)

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SOUND WAVES

Sound is the most common example of a longitudinal wave

In sound waves, the molecules of air transmit the vibrations through compressions and rarefactions

Sounds waves cannot travel in vacuum!

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SPEED OF SOUND

Speed of sound is affected by: wind conditions, temperature, humidity and type of medium NOT affected by its loundness (amplitude)

Sound travels faster in liquids and solids compared to gases Closely packed molecules in solids and liquids will transmit the

vibrations faster than in gases

Sound travels faster at higher T Faster moving air particles bump into each other more

frequently and carry vibrations in shorter time

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DOPPLER EFFECT

The apparent shift in pitch of sound when the source is moving relative to the observer is called the Doppler Effect

i.e. The sudden change in pitch of an ambulance siren as it goes by an observer is the result of the Doppler effect

Pitch of a sound is the subjective measure of its frequency High frequency sounds have high pitch, and low frequency sounds

have low pitch

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STANDING WAVES

Waves that are reflected on themselves and appear to “stand” are called standing waves

Standing waves produce the variety of sounds in musical instruments! (Animation) violin

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RESONANCE

Every object has natural vibrations caused by motion of its molecules

When a forced vibration matches an object’s natural vibrations, a dramatic increase in amplitude occurs This phenomena is called Resonance

Some Examples Tacoma Narrows Bridge Resonant Bridge

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THE END

Some Symbols Used

• all• there is or there exists• Change• infinity• multiplication• proportional to• less than or equal to• greater than or equal to• plus or minus• degrees• therefore• ≈ approximately equal to• decreases• increases

• λ – Wavelength• E – Energy• H – Heat• # - Number• e- - electron• p+ - proton