Sound Ch 17 the speed of sound traveling
- Slides: 24
Sound (Ch 17) • the speed of sound • traveling sound waves • interference – 和§ 16 -10 & § 35 -4 比較 • intensity & sound level – the Decibel Scale (d. B) • sources of musical sound • beats • Doppler effect
the speed of sound • 從看到閃電和聽到打雷估計閃電的高度 • Ch 17, Problem 7 (Home Work) :從地震 P 波(longitudinal)和 S 波(transverse)計算地震的發生處
traveling sound waves (§ 17 -4) • 比較二個振幅: – displacement amplitude Sm (空氣粒子實際運動的振幅) S(x, t) = Sm cos(kx-ωt) (17 -13) – pressure amplitude △Pm (壓力振幅) △P(x, t) = △Pm sin(kx-ωt) (17 -14) – △Pm 和Sm 相位相差π/2,見 Fig. 17 -5 & Fig. 17 -7 – △Pm = (vρω)Sm (17 -15)
Longitudinal wave • displacement amplitude Sm • pressure amplitude △Pm 和 Sm 相位相差π/2 △Pm = (vρω) Sm Transverse wave • wave speed (phase speed) • transverse speed (particle speed)
interference (§ 17 -5) • 和§ 16 -10 & § 35 -4 比較 • path length difference △L(波程差) & phase differenceψ – ψ = 2π△L /λ (17 -21) – fully constructive interference • ψ = 0, 2π, 4π, 6π, … (17 -22) • △L = mλ,m = 0, 1, 2, …. (17 -23) – fully destructive interference • ψ = π, 3π, 5π, 7π … (17 -24) • △L = (m+ ½)λ,m = 0, 1, 2, … (17 -25) Check Point 2 Sample problem 17 -3
Intensity (§ 17 -6) • intensity I 單位:?
Intensity (§ 17 -6) • intensity I 單位:? • intensity I 與 displacement amplitude Sm 之關係 • displacement amplitude Sm • pressure amplitude △Pm
Music sound(§ 17 -7) • • • Standing wave resonant frequency fundamental mode(first harmonic) second harmonic, third harmonic, … sample problem 17 -6:管子裡的聲音 • 為什麼從貝殼裡可以聽到海浪的聲音?
Standing sound(§ 17 -7) • Ch 17, Problem 37:小提琴 • Ch 17, Problem 41:用聲音測井的深度
Beats (§ 17 -8) 在某一點,二聲波之位移對時間的變化 S = S 1 + S 2 = S 1 cosω1 t + S 2 cosω2 t 利用三角恆等式 可得 (17 -43): S = 2 Smcos( ½ (ω1 -ω2)t) cos( ½ (ω1+ω2)t ) = 2 Smcos ω’t cos ωt (17 -45) ωbeat= 2ω’= ω1 -ω2 (Why? ) fbeat= f 1 - f 2 (17 -46) Fig 17 -18 Homework:證明 (17 -45) Home work:用Excel畫出 Fig 17 -18
Doppler effect (§ 17 -9) • Doppler (1803~1853),1842年提出 Doppler effect • Doppler effect 的公式推導 – 二項式定理 • Doppler effect for sound – 消防車 – 聲頻防盜器抓小偷 (Problem 53) – shock wave 震波(超音速飛機) • Doppler effect for light – 警察雷達測速器(用什麼波?) – red shift 紅位移
Doppler effect (Detector moving, Source Stationary) Stationary detector Moving detector Fig. 17 -20 Fig. 17 -21 (17 -52)
Doppler effect (Source moving, Detector Stationary) Eq. 17 -53 & 17 -54 Fig. 17 -22
Doppler effect for sound • detector moving ; source stationary • source moving ; detector stationary ± 怎麼取? toward means greater
Detector
補充例題 202 -1 偵測靠近的物體 A transmitter and receiver of waves contained in a single instrument. It is used to measure the speed u of a target object (idealized as a flat plate) that is moving directly toward the unit, by analyzing the waves reflected from the target. (a) Show that the frequency fr of the reflected waves at the receiver is related to their source frequency fs by where ν is the speed of the waves. (b) In a great many practical situations, u << v. In this case, show that the equation above becomes
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