exam for Electronic Engineering

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EE 1301: MODERN ELECTRONIC TECHNOLOGY

SESSION #26: SOUND WAVES

03/28/2018

Instructor: Joseph Cleveland, Ph.D. Email: [email protected]

Thought for the Day

One-fourth of the world’s population needs hearing assistance – they need hearing aids!

Electronic processing of sound wave is a critical part of treatment

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Topics

• Properties of (sound) waves (CP 122-128) – Wavelength

– Speed

– Period

– Frequency

• Sound Level and Intensity

• Complex waves – Harmonics

– Fourier series

• HW #8 online this afternoon: Due next Wed

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Wave Generation

• Frequency = cycles per second

• Period T = time for one cycle of the wave

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

Unit is Hertz (Hz)

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• A sound wave for concert A has a frequency of 440 cps or Hz

• The period is

. …

• The wavelength is / /

. …

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• A high audio pitch has a higher frequency and shorter period

than a low audio pitch

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Measuring Sould Levels

Sound Relative to Atmospheric Pressure

• Weight of column of air on 1 square inch

. ⁄

at sea level

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.

.

Note: 200 lb = 889.6 N

A

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Measurement as Pressure Amplitude

Measured in decibels (dB)

For . ⁄ the SPL is

. .

.

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Pressure A N/m2

SPL dB

Threshold of Hearing

Other Sound Source Levels

• Stun grenade: ~175 dB

/

/

/ .

• Shock wave: ~194 dB (killing pressure) /

/

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Measurement as Intensity (W/m2)

• In terms of energy and power

• For . ⁄

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Intensity W/m2

SPL dB

Meaning of Decibels

• If the power is doubled · log .

. , a 3 dB increase

• If the power is 10X · log

, a 10 dB increase

• If the power is cut in half · log ⁄

. . , a 3 dB decrease

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Sound Intensity Calculations …

• Example Suppose a sound wave has an intensity of

. / What is the intensity in dB?

· / /

·

·

What value of y makes ?

. so the intensity is .

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Adding Sounds

• What is the SPL experienced when you are subject to a sound from one speaker with SPL = 100 dB and from another with SPL = 110 dB? – This problem has a hidden difficulty!

a) If the two sounds have the same or “almost” the same frequency, we add the pressures then use

b) If the two sounds have different frequencies or look like “noise, we add intensities then use

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Waves and Resonance

A Definition

• Resonance is a phenomenon in which a vibrating system or external force drives another system to oscillate with greater amplitude at a specific preferential frequency.

• Resonance occurs when a system is able to store and easily transfer energy between two or more different storage modes. – Waves traveling in opposite directions

– Energy stored in an inductor and in a capacitor

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Wave Interactions

• The two pulses, y1 & y2, with elements of positive displacement are traveling in opposite directions with same speeds

• Waves start to overlap, the resultant wave function is y1 + y2

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Wave Interactions …

• When crest meets crest the resultant wave has a larger amplitude than either of the original waves

• The two pulses separate They continue moving in their original directions The shapes of the pulses remain unchanged

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Wave Interactions …

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Two pulses are traveling in opposite directions. Their displacements are inverted with respect to each other.

When they overlap, their displacements partially cancel each other

Standing Waves and Resonance

• Now consider adding two sine waves, one moving right, one moving left (animation)

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Lee Amosslee, “Standing Waves and Resonance”, http://academic.greensboroday.org/~regesterj/potl/Waves /DiffractionInterference/StandingWave.htm

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Standing wave resonance in string

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Standing Waves and Resonance

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http://hyperphysics.phy- astr.gsu.edu/hbase/waves/string.html

Harmonic Resonances: why overtones exist

L

⁄

⁄

⁄

⁄

⁄

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Add Harmonic Waves

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100 Hz

 200 Hz

 300 Hz

5

1.5

2.5

Composite Wave

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Result

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Musical Sounds

• What allows us to recognize different instruments? – By the complex wave each produces as a unique

combination of harmonics

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Flute.nonvib.pp.C6Bb6.aiff

Trumpet.vib.pp.C6D6.aiff

Spectra of Musical Sounds

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Waveform

Harmonic #

Spectrum

Harmonic #

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Musical Instrument Sounds …

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The cello Cello.arco.ff.sulA.A3B3.aiff

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End of Session