Review: Sound Waves. Sound: The speed of the longitudinal sound wave is. elastic. v = (string, τ = tension, µ = linear mass density)

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1 Reiew: Sound Wae Sound Wae: Sound wae are longitudinal wae (i.e. inole ocillation parallel to the direction o the wae trael) that propagate through a medium (e.g. air, water, iron). Speed o Sound: The peed o any mechanical wae depend on both the inertial property o the medium (tore kinetic energy) and the elatic property (tore potential energy). elatic (wae peed) inertial Stretched String (Chapter 11): The peed o the tranere wae along a tretched tring i τ (tring, τ tenion, µ linear ma denity) µ Sound: The peed o the longitudinal wae i B (, B bulk modulu - P/( V/V), ρ olume ma ρ denity) Unierity o Florida Source S Medium Air (20 o C) Water (20 o C) Steel Sound Speed (m/) 343 1,482 5,941 Waeront PHY 2053 Page 1 Ray Medium ocillation Sound Speed (mi/hr) 768 3,320 13,308

2 Reiew: Sound Wae Traeling Sound Wae in Air: A traeling wae conit o a moing periodic pattern o expanion and compreion o the air. A the wae pae the air element ocillate longitudinally in imple harmonic motion. (1000 Hz wae with P max at the threhold o pain!) Longitudinal diplacement Preure ariation ( x, t) max co( kx ωt) P( x, t) Pmax in( kx ωt) Unierity o Florida P ( νρω max ) max (The preure amplitude i related to the diplacement amplitude!) PHY 2053 Page 2

3 Reiew: Intenity and Leel Intenity: Traeling wae tranport energy (kinetic and potential) rom one point to another. The intenity, I, o a wae at a urace i the aerage energy per unit time per unit area tranmitted by the wae to the urace (i.e. aerage power per unit area). It i alo equal to the aerage energy per unit olume in the wae time the peed o propagation o the wae. Watt/m 2 I 1 A de dt Unierity o Florida P power A I de dv ρω max 2 Variation with itance: I i emitted iotropically (i.e. equal intenity in all direction) rom a point ource with power P and i the mechanical energy o the wae i conered then P I (intenity rom iotropic point ource) 2 4πr The ecibel Scale: Intead o peaking about the intenity I o, it i more conenient to peak o the leel β, where β ( 10dB)log10( I / I0) I I0 10 β /10 db ( leel, db decibel, I W/m 2 ) 2 P ρ max (the intenity i proportional to the quare o the amplitude!) Sound Hearing threhold Source P S Coneration Pain threhold PHY 2053 Page 3 r leel (db) Sphere with radiu r Intenity (W/m 2 )

4 Sound Wae: oppler Eect oppler Shit: I either the detector or the ource o i moing, or i both are moing, then the emitted requency,, o the ource and the detected requency, ob, are dierent. I both the ource and the detector are at ret with repect to the air and λ i the peed o in air then N t / λ pule ob t t λ the peed o in air then N pule ( t + t) / λ + ob t t λ (ource tationary, detector tationary) etector Moing, Source Stationary: I ource i at ret and the detector i moing toward the ource with peed with repect to the air and λ i + / + (ource tationary, detector moing toward the ource) (Source and detector at ret) (Source at ret, etector moing toward the ource) ob Unierity o Florida ± (ource tationary, detector moing toward (+) or away (-) rom the ource) PHY 2053 Page 4

5 Sound Wae: oppler Eect etector Stationary, Source Moing: I detector i at ret and the ource i moing toward the detector with peed with repect to the air and λ i the peed o in air and T 1/ i the time between emitted pule then ob λ T T / / ob ob ob ollowing our poibilitie: + Source m Unierity o Florida (detector tationary, ource moing toward the detector) (detector tationary, ource moing toward (-) or away (+) rom the ource) (detector tationary, ource moing toward the detector) etector and Source Moing: I detector i moing with peed and the ource i moing with peed with repect to the air then there are the ob Source etector etector ob ob Source Source etector etector PHY 2053 Page 5

6 Summary: oppler Eect etector and Source Moing: I detector i moing with peed and the ource i moing with peed, and λ i the peed o in air then the obered requency at the detector i ob Take poitie i the detector i moing in the direction o the propagation o the wae. Take negatie i the detector i moing oppoite the direction o propagation o the wae. Take poitie i the ource i moing in the direction o propagation o the wae. Take S negatie i the ource i moing oppoite the direction o propagation o the wae. Unierity o Florida PHY 2053 Page 6

7 oppler Eect: Example A low lying airplane kim the ground at a peed o 200 m/ a it approache a tationary oberer. A loud horn whoe undamental requency i 400 Hz i carried on the plane. What requency doe the ground oberer hear? (Aume that the peed o in the air i 343 m/.) Anwer: 959 Hz 1 400Hz ob 959Hz 1 / 1 (200 / 343) I intead the horn were on the ground, what requency would the airplane pilot hear a he approached? Anwer: 633 Hz ob + ( / 343)(400Hz) (1 + / 633Hz ) Unierity o Florida PHY 2053 Page 7

8 oppler Eect: Example The pitch o the rom a race car engine drop the muical interal o a ourth when it pae the pectator. Thi mean the requency o the ater paing i 0.75 time what it wa beore. How at i the race can moing? (Aume that the peed o in the air i 343 m/.) Anwer: 49.0 m/ toward away + ξ away toward + 1 ξ (343m / ) 49.0m / 1+ ξ Unierity o Florida PHY 2053 Page 8

9 oppler Eect: Example A tationary motion detector end wae o requency o 600 Hz toward a that i peeding away. The wae ent out by the detector are relected o the and then are receied back at the detector. I the requency o the wae receied back at the detector i 400 Hz, what i the peed o the receding (in m/)? (Take the peed o to be 343 m/.) Anwer: 68.6 m/ Part 1: The i the detector and i the requency obered by the and 0 i the original requency emitted by the motion detector which i the ource. ob + + Part 2: The i now the ource emitting requency and the motion detector i the detector which obere requency ob. 0 0 ob 0 + Unierity o Florida 0 ob 600Hz 400Hz (343m / ) 0 + ob 600Hz + 400Hz 68.6m / PHY 2053 Page 9