Sound II. Sound intensity level. Question. Energy and Intensity of sound waves

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Norma Anthony
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Soud. Eergy ad tesity terferece of soud waes Stadig waes Complex soud waes Eergy ad tesity of soud waes power tesity eergy P time power P area A area A (uits W/m ) Soud

The ear is capable of distiguishig a wide rage of soud itesities. β 0log o o β 0 0 What is the itesity of soud at a rock cocert?

1 Soud. Eergy ad tesity terferece of soud waes Stadig waes Complex soud waes Eergy ad tesity of soud waes power tesity eergy P time power P area A area A (uits W/m ) Soud itesity leel β 0log o o 0 - W/m decibels (db) the threshold of hearig decibel is a logarithmic uit. t coers a wide rage of itesities. The ear is capable of distiguishig a wide rage of soud itesities. β 0log o o β 0 0 What is the itesity of soud at a rock cocert? (W/m ) β 0log 0 o 0 log Questio Questio The soud itesity of a ipod earphoe ca be as much as 0 db. How is this possible? A) The ipod is ery powerful B) The area of the earphoe is ery small C) The ipod is a digital deice D) Rock music ca be ery loud W/m

The soud itesity of a ipod earphoe ca be as much as 0 db. How is this possible? Spherical ad plae waes A 4πr area of sphere The earphoe is placed directly i the ear.

2 The soud itesity of a ipod earphoe ca be as much as 0 db. How is this possible? Spherical ad plae waes A 4πr area of sphere The earphoe is placed directly i the ear. The itesity at the earphoe is the power diided by a small area. Say the area is about cm. 4 4 P A w /m (0 m ) 0 W A small amout of power produces a high itesity. For a poit source the itesity decreases as /r P 4 π r P power of source Suppose you are stadig ear a loudspeaker that ca is blastig away with 00 W of audio power. How far away from the speaker should you stad if you wat to hear a soud leel of 0 db. ( assume that the soud is emitted uiformly i all directios.) terferece of soud waes Two soud waes superimposed Costructie terferece P P A 4 π r r P 4π 00W.8m 4 π(w/m ) Destructie terferece Noise cacelig headphoes Noise Wae Wae Ati-oise Wae Wae terferece due to path differece r r phase at x0 path differece δ r r Coditio for costructie iterferece Coditio for destructie iterferece A where m is ay iteger Superpositio of waes at A shows iterferece due to path differeces δ m δ ( m + ) m 0 +, +,.

δ0 terferece Costructie terferece δ terferece Destructie terferece Sum δ terferece Costructie terferece terferece of soud waes Phase shift due to path differeces x Whe r r m Costructie terferece Whe

legths ad combiig them at the detector. For a frequecy of.0 khz (assume soud 40 m/s); A) What would the smallest path differece be to obsere a miimum i itesity r r f 40m / s (x0 s ) 5.

3 δ0 terferece Costructie terferece δ terferece Destructie terferece Sum δ terferece Costructie terferece terferece of soud waes Phase shift due to path differeces x Whe r r m Costructie terferece Whe r r (m+½) Destructie terferece m is ay iteger Example A experimet is performed to measure the speed of soud usig by separatig the soud from a sigle source alog two separate paths with differet path legths ad combiig them at the detector. For a frequecy of.0 khz (assume soud 40 m/s); A) What would the smallest path differece be to obsere a miimum i itesity r r f 40m / s (x0 s ) 5.7cm B) What would the smallest (o-zero) path differece be to obsere a maximum i itesity. r r cm Example 4.6 Path differece for two sources. r -r 0. m At positio P the listeer hears the first miimum i soud itesity. Fid the frequecy of the oscillatio. soud 40 m/s At positio P the path differece is equal to /. (first miimum) destructie iterferece. r r 0.m (0.) 0.6m 40m/ s f.x0 Hz 0.6m

Stadig Wae Stadig Waes Stadig waes (waes o a strig) Stadig waes i air colums.

The stadig wae stores eergy of waes with specific waelegths. Stadig wae o a strig Nodes Stadig Wae with odes At differet times.

same frequecy ad waelegth traelig i opposite directios.

4 Stadig Wae Stadig Waes Stadig waes (waes o a strig) Stadig waes i air colums. A stadig wae is formed by reflectios back ad forth at the boudaries of a media. The stadig wae does ot carry eergy but seres to store eergy. The stadig wae stores eergy of waes with specific waelegths. Stadig wae o a strig Nodes Stadig Wae with odes At differet times. The Stadig wae does t moe it just stads i oe place Ati-odes Fixed ed Stadig Waes A stadig wae is geerated by superpositio of two waes with the same frequecy ad waelegth traelig i opposite directios. Stadig Wae Coditios Oe ode at each ed with additioal odes oly at specific positios Distace betwee odes / Simulatio of a stadig wae. A strig with legth ca support stadig waes of oly at certai waelegths. where,, iteger alues called the fudametal called the secod harmoic etc. 4

Stadig wae frequecies ad waelegths f Example Fid the fudametal ad secod harmoics of a steel wire fixed at

.. Stadig waes i air colums Fudametal Frequecy eds closed eds ope oe ed ope oe ed closed N N A A N A Cylider

.. All harmoics Cylider ope at oe ed closed at oe ed - Harmoics Summary For a cylider with the same legth f

5 Stadig wae frequecies ad waelegths f Example Fid the fudametal ad secod harmoics of a steel wire fixed at both eds. The speed of the wae i the strig is 00 m/s f f 00 00Hz () f 00 Hz where,,... Stadig waes i air colums Fudametal Frequecy eds closed eds ope oe ed ope oe ed closed N N A A N A Cylider ope at both eds Harmoics 4 F F F is the speed of soud i air F lower by a factor of f f,,, 4... All harmoics Cylider ope at oe ed closed at oe ed - Harmoics Summary For a cylider with the same legth f f,, 5, 7... Oly odd harmoics Frequecy 5f 4f f f f 0 f 7f f 5f f f f f,,...,, 5... f oly odd harmoics all harmoics 0 both eds ope/ closed oe ope oe closed 5

Example A cylider 5.0 cm i legth is closed at oe ed ad ope at the other ed.

05)m Frequecy due to stadig waes o the strig. The body of the istrumet acts as a resoator to moe air to amplify the soud.

soud waes are a combiatio of differet frequecies.

6 Example A cylider 5.0 cm i legth is closed at oe ed ad ope at the other ed. Fid the frequecy of the third harmoic of the stadig wae i the colum. air 40 m/s f Strig strumets Musical strumets f f (40)m / s 5.x0 Hz 4(0.05)m Frequecy due to stadig waes o the strig. The body of the istrumet acts as a resoator to moe air to amplify the soud. Wid istrumets Musical strumets The soud is produced by ibratig air ad the frequecy is ehaced by resoace i the air colum Complex waes geeral soud waes are a combiatio of differet frequecies. The superpositio of waes with differet frequecies gies rise to the characteristic quality (timbre) of the soud. The differet frequecies ca be determied by mathematical procedure called a Fourier Trasform. Complex waes cosist of differet frequecy compoets, i.e. harmoics. displacemet relatie amplitude Time Frequecy 6

Physics 231 Lecture 28

Physics 231 Lecture 28 Physics 31 Lecture 8 Cocepts or today s lecture Spherical waes P I 4πr Dopper shit + o ƒ' ƒ s Itererece o soud waes L L λ costructi e ( 0,1,) L 1 1 L ( + 1/ ) λ destructi e Stadig waes o strig: L λ L 1,,3,,,