James T. Shipman

Jerry D. Wilson

Charles A. Higgins, Jr.

Omar Torres

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Waves and Sound

Chapter 6

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• We know that when matter is disturbed, energy emanates from the disturbance. This propagation of energy from the disturbance is known as a wave.

• Waves transfer energy form place to place but do not transfer matter (in general)

Section 6.1

Waves

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Longitudinal Wave: (sound):

Section 6.2

Longitudinal & Transverse Waves

There are two types of waves, classified based

on their particle motion and wave direction:

The particle motion and the wave velocity have the same direction

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Transverse Wave (light):

Longitudinal & Transverse Waves

The particle motion is perpendicular to the direction of wave velocity

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• Wavelength (l) – the distance of one complete wave

• Amplitude – the maximum displacement of any part of the wave from its equilibrium position

Section 6.2

Wave Description

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Period and Frequency

Period (T ) : the time it takes for a wave to travel a one wavelength

Frequency ( f ) : the number of oscillations during 1s, its unit is hertz (Hz)

• Frequency and Period are inversely proportional,

1f

T

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Period and Frequency

Find the period and Frequency for each wave?

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• Since speed is distance/time:

v = l/T or v = lf,

v = wave speed (m/s)

l = wavelength (m)

T = period of wave (s)

f = frequency (Hz) Section 6.2

Wave Speed (v)

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A sound wave has a speed of 344 m/s and a wavelength of 0.500 m. What is the frequency of the wave?

Solution:

Rearrange formula (v = lf ) to solve for f = v/l

f = v/l = (344 m/s)/(0.500 m/cycle)

f = 688 cycles/s

Section 6.2

Calculating Frequency – Confidence Exercise

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• Consist of vibrating electric and magnetic fields that oscillate perpendicular to each other and the direction of wave propagation. The speed of electromagnetic waves is

c = 3.00×108 m/s

Section 6.3

Electromagnetic Waves

A

-A

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Electromagnetic (EM) Spectrum

If the wavelength of a microwave beam is 11.5 cm, then what is the frequency of the radiation?

83.0 10 /

111.5

100

c m sf

mcm

cm

l

11 12.6 10 s

Computing Microwave Frequency

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What is the wavelength of the radio waves produced by a station with an assigned frequency of 600 kHz?

Solution:

f = 600 kHz = 600×103 Hz = 6.00×105 Hz

Rearrange equation (c = lf ) and solve for l

l = c/f = (3.00×108 m/s)/(6.00×105 Hz)

l = 0.500×103 m = 500 m

Section 6.3

Computing Radio Wave Wavelength

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Calculating visible wavelengths

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Sound Waves

• Sound:

− the propagation of longitudinal waves through matter (solid, liquid, or gas)

− The vibration of a tuning fork produces a series of compressions (high pressure regions) and rarefactions (low pressure regions)

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• Similar to the electromagnetic radiation, sound waves also have a spectrum

• The sound spectrum can be divided into three frequency regions:

– Infrasonic, f < 20 Hz

– Audible, 20 Hz < f < 20 kHz

– Ultrasonic, f > 20 kHz

Section 6.4

Sound Spectrum

• The audible region for humans is about 20 Hz to 20 kHz

• Sounds can be heard due to the vibration of our eardrums caused by the sound waves propagating disturbance

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• Loudness or Sound intensity (I) is the rate of energy transfer through a given area, has a unit of J/s/m2 or W/m2

• Sound Intensity decreases inversely to the square of the distance from source (I 1/r2)

Section 6.4

Sound Intensity

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• Sound Intensity is measured on the decibel scale

• A decibel is 1/10 of a bel (in honor of Alexander Graham Bell)

• The decibel scale is not linear with respect to intensity

Section 6.4

Decibel Scale

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The Doppler Effect Illustrated

The Doppler effect: the apparent change in frequency resulting from the relative motion of the source and the observer

Higher frequency Lower Frequency

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• As a moving sound source approaches an observer, the waves in front are bunched up and the waves behind are spread out due to the movement of the sound source

• The observer hears a higher pitch (shorter l) as the sound source approaches and then hears a lower pitch (longer l) as the source departs

Section 6.5

The Doppler Effect

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• As the jet approaches the speed of sound, compressed sound waves and air build up and act as a barrier in front of the plane

• As a plane exceeds the speed of sound it forms a high-pressure shock wave, heard as a ’sonic boom’

Section 6.5

Sonic Boom

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• Standing wave – a “stationary” waveform arising from the interference of waves traveling in opposite directions

– When these two waves meet they constructively “interfere” with each other, forming a combined and standing waveform

Section 6.6

Standing Waves

λ

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• When one tuning fork is struck, the other tuning fork of the same frequency will also vibrate in resonance

• The periodic “driving force” here are the sound waves Section 6.6

Resonance

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Homework (Exercises)

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