Physics 231 Lecture 27

Transcription

1 Physics 31 Lecture 7 Concepts for today s lecture Wae speed for a string / μ : tension; μ m /L. Sound intensity I β 10log 10 I 0 IP/A, I 0 μ 1x10-1 W/m Spherical waes Here P is the string tension I and μ is 4πr the mass/lengt h. Dopper shift ƒ' ƒ + o s

2 Wae elocity on string Waes trael faster on strings with higher h tension and lower mass/unit length. The exact relationship is Here μ is the string tension and μ is the mass/lengt Example: A 0.5 m string is stretched so the tension is 1.7 N. A transerse wae of frequency 10 Hz and waelength 0.31 m traels on the string. What is the mass of the string? (Hint: use wae elocity to get mass.) m μl; λf μ L 0.5m; ( )( ) μ μ 0.31m 10Hz 37.3m / s 1.7N 3 1.x10 kg /m 37.3m / s ( ) ( 3 )( ) m μl 1.x10 kg/m 0.5m 0.61g h.

3 Example Problem A particular species of spider spins a web with silk threads of density 1300 kg/m 3 and diameter 3.0 µm. A typical tension in the radial threads of such a web is N. What is the speed of the waes traeling on the web. If a fly lands in this web, which will reach the spider first, the sound or the wae on the web silk? (sound elocity343 m/s) a) 17 m/s, no b) 15 m/s, no c) 86 m/s. no d) 430 m/s, yes 3 e) 873 m/s, yes ρ 1300kg /m M ρv ρasilkl 3 6 μ M/L ρ A silk ( 1300kg / m ) (3x10 m/) x10 kg /m.007kg m / s 9 μ 9.19x10 kg / m 873m / s This is faster than the speed of sound in air. Slide 15-1

4 Conceptual question A weight is hung oer a pulley and attached to a string composed of two parts, each made of the same material but one haing four times the diameter of the other. The string is plucked so that a pulse moes along it, moing at speed 1 in the thick part and at speed in the thin part.what is 1 /? M Vρ πrlρ μ M/L πr ρ μ π ρ 1 R1 1 πr 1 1ρ R R 1 R R 1/4 1 R R 1 R1 πr ρ R

5 Using a Tuning ork to Produce a Sound Wae A tuning fork will produce a pure musical note of frequency f As it s tine swings to the right, it forces the air molecules near it closer together This produces a high density area in the air This is an area of compression As the tine moes toward the left, the air molecules to the right of the tine spread out This produces an area of low density This area is called a rarefaction As the tuning fork continues to ibrate, a sinusoidal succession of compressions and rarefactions spread out from the fork Crests correspond to compressions and troughs to rarefactions λf λ

6 Sound Waes Audible range: between 0 Hz to 0, Hz Infrasonic waes: f < 0 Hz; Ultrasonic: f > 0,000 Hz Sound elocity : elastic _ property inertial _ property Sound elocity in solid: Y ; Y ρ is Young' s modulus Sound elocity in liquids or gasses: B ; B is ρ the bulk modulus Sound elocity in air: ( 331m / s) T ; T is in Kelin 73K 331m / s + (0.60m / s / C) T Here, T is in Celcius. T (in Kelin) T (in Celcius) +73

7 s,water air Example You are watching a pier being constructed on the far shore of a saltwater inlet when some blasting occurs. You hear the sound in the water 4.50 s before it reaches you through the air. How wide is the inlet? (Assume the air temperature is 0 C and sound elocity in water is 1530 m/s at its temperature (5 C). ) 1530m/s; ( 331m / s) t d/ ; s,air s,air water s,water T 73K 331m / s 343m / s 73 ( ) 93 t ( ) air t water d 1/ s,air 1/ s,water t d/ ; ( ) ( ) air water s,air s,water d t t / 1/ 1/ s / 1989m 343m / s 1530m / s

8 Quiz Ad dolphin located din sea water at a temperature t of f5 C emits a sound directed toward the bottom of the ocean 150 m below. How much time passes before it hears an echo? (The sound elocity in sea water 1530 m/s at 5 0 C) C.) a)0. s b)0.4 s c)0.6 s d)0.8 s t d/ e) 0.1 s Δ 300m / (1530m / s) 0.196s

9 Sound amplitude and intensity The amplitude of the sound wae is proportional to the maximum elocity of the air as it moes from the high pressure to the low pressure domains. The energy and the power of the sound wae is proportional to the square of amplitude: 1 E ρ Amplitude max p xmax More useful than the energy of a sound wae is the intensity, I, which is the power P that the sound wae transmits per unit area. I P E A Δ AΔT The ear responds logarithmically to the intensity of sound waes striking the eardrum. I threshold I W/m, I pain 1 W/m ( ) This logarithmic behaior motiates the decibel measure of sound wae intensity. ig 14., p. 46 Slide 4 β10 log 10 (I/ I 0 ) β/10 log 10 (I/ I 0 ) 10 β/10 I/I 0

10

11 Example The intensity leel of sound A is 4.0 db greater than that of sound B. Dt Determine the ratio (I A /I B ) of fthe intensity it of sound to the intensity it of sound B. X I log β 10log 10 log10 ( X) log10 ( Y) 10 Y I I I 4 β β 10log 10log β A A B A B I 0 I 0 β B ( ) g ( ) 10log I 10log I 10 A 10 B 10log ( I ) 10log ( I ) 10 log I 10 log I I 0 10 A 10 0 A 10 log 10 4 I B ( ) ( ) ( 10 log ( I 10 B ) 10 log 10 ( I 0 )) I A A log I IB B I A