Chapter 12 Sound Waves. We study the properties and detection of a particular type of wave sound waves.

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1 Chapter 2 Soud Waves We study the properties ad detectio o a particular type o wave soud waves. A speaker geerates soud. The desity o the air chages as the wave propagates. Notice that the displacemet maxima ad miima occur where the pressure variatio is zero ad the pressure variatio maxima ad miima occur where the displacemet is zero. The rage o requecies that ca be heard by humas is typically take to be betwee 20 Hz ad 20,000 Hz. Most people struggle to hear the highest requecies ad that ability lesses with age. Speed o Soud Recall v Restorig Force ertia luids 2-

2 v B The speed o the wave i a luid (especially air) depeds o temperature. solids v Y Amplitude ad tesity o Soud Waves A soud wave ca be described either by talkig about pressure or displacemet. Sice the displacemet creates the pressure chage, there is a relatioship betwee the amplitude o the pressure p0 ad the amplitude o the displacemet s0. For a harmoic soud wave the relatio is p v 0 s 0 A larger amplitude wave appears louder, but the relatio betwee amplitude ad loudess is very complicated. Loudess is subjective ad depeds o the respose o the ear ad the brai. Usually the itesity ad ot the amplitude is used or loudess. Agai or a harmoic wave 2 0 p 2v The most importat thig to remember is that itesity is proportioal to the amplitude squared, which is true or all waves, ot just soud. (p 425) 2-2

3 Decibel Scale The perceptio o hearig is roughly proportioal to the logarithm o the itesity. The lowest itesity o soud that ca be heard by most people is W/m 0 is called the threshold o hearig. t is used as the reerece level or measurig soud itesity. The soud itesity level i decibels is deied as (0 db)log 0 0 (Be sure to practice with the decibel scale. Logarithms ca be tricky.) A itesity level o 0 db correspods to the threshold o hearig. For icoheret soud waves with itesities ad 2, the total itesity is 2 the soud waves are coheret, the waves ca iterere ad the itesity is betwee 2 ad + 2, depedig o the phase relatioship betwee the two waves. Decibels ca be used i a relative sese. The dierece i two db readigs 2-3

(0 db)log 2 (0 db)log 0 0 2 0 2 (0 db)log 0 0 is related to the ratio o the itesities. Stadig Soud Waves Recall that a stadig wave is the superpositio o two travelig waves.

4 (0 db)log 2 (0 db)log (0 db)log 0 0 is related to the ratio o the itesities. Stadig Soud Waves Recall that a stadig wave is the superpositio o two travelig waves. The wave relects at the boudary o the wave. Pipe ope at Both Eds The boudary coditios are the same at both eds. Sice the ed is ope to the atmosphere, the pressure at the eds ca ot deviate much rom atmospheric pressure. The eds are pressure odes. Pressure odes are displacemet atiodes. From the diagram, the wavelegths satisy 2L The requecies v v 2L The idex is a iteger ad it ca vary rom, 2, etc. 2-4

5 Pipe Ope at Oe Ed The situatio is dieret rom the pipe opeed at both eds. The closed ed is a pressure atiode. The air at the closed ed is isolated rom the atmosphere ad the pressure ca deviate ar rom atmospheric. The air at the closed ed is a displacemet ode sice the rigid wall prevets the air rom movig. From the diagram, the wavelegths satisy 4L The requecies v v 4L This time has odd values oly (, 3, 5, etc.) 2-5

6 Problem 27 Two tuig orks A ad B, excite the ext-to-lowest resoat requecies i two air colums o the same legth, but A s colum is closed at oe ed ad B s colum is ope at both eds. What is the ratio o A s requecy to B s requecy. Sice A excites the pipe ope at oe ed, oly the odd harmoics are possible v v 4L Where =, 3, 5, etc. Next to lowest resoat requecy reers to the secod requecy. Here that mea = 3 ad A v v 3 4L 4L For B, all the harmoics are possible sice it is excitig a pipe ope at both eds. v v 2L =, 2, 3, etc. Next to lowest i this sequece correspods to = 2, v v B 2L 2 2 L Formig a ratio A B v 3 4L v 2 2L 3v 2L 4L 2v 3 4 Timbre geeral, a musical istrumet will produce souds that are made o combiatios o the available requecies. The lowest requecy i a complex soud wave is called the udametal ad the other requecies are called overtoes. Sice all the overtoes are itegral multiples o the udametal, they are also called harmoics. The complex shape o the soud wave meas that dieret istrumets playig the same ote will have a dieret toe quality. You ca recogize your avorite siger by the timbre o the siger s voice. 2-6

7 A complex periodic sigal ca be created by addig together a set o harmoic waves. The wave havig three requecies 0, 65, ad 220 Hz repeats at 55 Hz sice each o these requecies are harmoics o 55 Hz. priciple, ay complex waveorm ca be decomposed ito a series o harmoic waves. This is called Fourier (or spectral) aalysis. Limitig our study to harmoic waves actually icludes all waveorms. 2-7

Huma Ear The physiology o the ear is detailed i the text. Please read it. A brie overview o the ear: http://www.youtube.com/watch?v=p3oy4lodzu4 The perceptio o loudess depeds o requecy.

8 Huma Ear The physiology o the ear is detailed i the text. Please read it. A brie overview o the ear: The perceptio o loudess depeds o requecy. Pitch is the perceptio o requecy. Higher pitch meas higher requecy (ad shorter wavelegths). Beats occurs whe two soud waves are close i requecy. t is very useul or tuig istrumets. The beat requecy is the dierece i the two requecies 2-8

beat 2 The Doppler Eect Probably best explaied i http://www.youtube.com/watch?

9 beat 2 The Doppler Eect Probably best explaied i Or ot! Maybe this will work? The Doppler eect is the chage i observed requecy (pitch) resultig rom the motio o the soud source ad/or soud observer. t ca be used to measure the speed o a movig car (or baseball). rot o the movig source, the wave crests are closer together ad the requecy is higher. Behid the movig source, the wave crests are urther apart ad the requecy is lower. O vs v / S mportat: vs > 0 or a source movig i the directio o the wave. 2-9

away rom the source will experiece a lower requecy.

10 A observer movig relative to a statioary source will experiece a dieret requecy. A observer movig towards the source will experiece a higher requecy ad a observer movig away rom the source will experiece a lower requecy. ( v / v) O O S mportat: vo > 0 or a observer movig i the directio o the wave. both the source ad observer move O v v O S / v v / S 2-0

11 The sig covetio is give or the idividual cases. You must get the sigs right to get the correct aswer!! Shock Waves Whe the source moves aster tha the speed o soud, the wave crests pile o top o each other ad a large amplitude wave occurs. For airplaes, this is called a soic boom. Shock waves: Echolocatio ad Medical magig Soud ad echoes are used to locate objects. Here is a aimatio explaiig soar: Ultrasoud ca be used to image structures iside the body. 2-

12 High requecy soud is used sice higher requecies will have shorter wavelegths. Short wavelegths diract less aroud small obstacles. Time or the ed o the semester music estival. 2-2

GENERATE AND MEASURE STANDING SOUND WAVES IN KUNDT S TUBE.

Acoustics Wavelegth ad speed of soud Speed of Soud i Air GENERATE AND MEASURE STANDING SOUND WAVES IN KUNDT S TUBE. Geerate stadig waves i Kudt s tube with both eds closed off. Measure the fudametal frequecy