Chapter 17: [Sound] Waves-(II) In Halliday and Resnick: Longitudinal waves are sound waves! We categorize sound waves according to their frequency into: Audible Infra Sonic Ultrasonic Mathematica: Play sound Sound waves propagate in gases. Can they propagate in liquids and/ or solids? Note: presentation main figures are that of Halliday and Resnick 6th edition unless otherwise specified.

17.2 Sound Waves: (cont’d) The circles should really be spheres (in three dimensions). Note that the rays are perpendicular to the wavefronts and indicate the direction of propagation.

17.2 Sound Waves: (cont’d) Applications of sound waves: hearing sounds probing for oil sea floor topography submarine positioning ultrasound to image human body. In chapter 18, we concentrate on sound waves that travel through air and are audible.

(elastic property/inertial property)1/2 So, v = (B/r)1/2 17.3 The Speed of Sound: Speed of sound waves: (elastic property/inertial property)1/2 So, v = (B/r)1/2 Is B larger for steel or for mercury? Is B larger for water or for air? Example: What is the speed of sound in an aluminum rod. Hint: BAl = 7x1010 N/m2; rAl = 2.7 gm/cm3. v = 5091 m/s

Dp(x,t) = Dpm sin(kx-wt) 17.4 Traveling Sound Waves: Periodic sound waves: s(x,t) = sm cos(kx-wt) Dp(x,t) = Dpm sin(kx-wt) Dpm = r v w sm Example: (a) What is the wavelength of 600 Hz frequency sound waves in an aluminum rod. (b) If the overpressure amplitude is 5.24 Pa, describe the displacement as a function of space and time. lambda = 8.485 m Omega = 3770 Hz sm = 1.01 10(-10) m = 1.01 angstom k = 0741 m-1

17.4 Traveling Sound Waves: (cont’d) Notice how s(x,t) and Dp(x,t) are 90o out of phase. See Mathematica pressure and displacement code (AJ)

17.5 Interference: Interference, path lengths, phase difference: DL = |L2 – L1| DL/l = f/2p constructive interference (maximum sound): DL/l = 0, 1, 2, ... etc. destructive interference (minimum sound): DL/l = 0.5, 1.5, 2.5, ... etc.

17.5 Interference: (cont’d) Example: If the distance between the two sources [centered about the origin] is 1.5 l, at how many places will there be constructive interference on the circumference of the circle? What about destructive interference? Interaction: at how many places will there be destructive interference if distance between the two sources is 0.5 l?

17.6 Intensity and Sound Level: Intensity: power per unit area. I = P/A The rate at which the energy being transported by the wave flows through a unit area perpendicular to the direction of travel of the wave. I = ½ r v (w sm)2 = Dp2m/(2rv) What is the threshold of hearing? What is the threshold of pain? How much sound energy per unit area impinges on your ears in a normal conversation?

17.6 Intensity and Sound Level: (cont’d) How does the intensity vary with distance from the source? The intensity falls as 1/r2 (why??) Spherical and plane waves: How does a small part of a spherical waves look like at large distances? Looks like a plane wave!

17.6 Intensity and Sound Level: (cont’d) What is Io? Io = 10-12 W/m2 Treshold of hearing! Sound level (in decibel): = 10 log(I/Io) Example: Find the sound level of the threshold of pain. 120 10(-4) Example: What is the intensity of an 80 dB sound?

17.6 Intensity and Sound Level: (cont’d) As a rule of thumb: Every increase by a factor of 10 in intensity is an increase in sound level by 10 dB. Every decrease by a factor of 10 in intensity is an decrease in sound level by 10 dB. Every increase by a factor of 2 in intensity is an increase in sound level by 3 dB. Every decrease by a factor of 2 in intensity is an decrease in sound level by 3 dB. 32 Can you prove it? Question: how much more intense is a 72 dB sound than a 57 dB sound?

17.7 Sources of “Musical” Sound: Remember from chapter 17: Standing waves in a string: (n: integer) ln = 2L/n fn = v/ln fn = nv/2L fn = (n/2L) (F/m)1/2 fn = n f1 (harmonic series) There is “Resonance” at the frequencies fn !! What is so great about resonance? There is Large, Sustained amplitude!

17.7 Sources of “Musical” Sound: (cont’d) The same is true for air columns!! Standing waves in air columns: Displacement node (i.e. pressure antinodes) at closed end. Displacement antinodes (i.e. pressure nodes) at open ends. Air reflects at open and at closed ends!!

17.7 Sources of “Musical” Sound: (cont’d) A- Column open at both ends [or closed at both ends]: nth harmonic has frequency: fn = nv/2L (n = 1, 2, 3, …) Or, fm = mv/4L (m = 2, 4, 6, …) 637.5 Hz Example: an 80 cm sound column open at both ends is vibrating at its third harmonic. What is its frequency? Hint: (speed of sound in air is 340 m/s)

17.7 Sources of “Musical” Sound: (cont’d) B- Column closed at one end and open at the other end: nth harmonic has frequency: fn = nv/4L (n = 1, 3, 5 …) Note: odd n only!!

17.7 Sources of “Musical” Sound: (cont’d)

17.9 The Doppler Effect: Doppler effect: what happens when source and/ or detector are moving? [assume the medium (air) to be stationary] Use top sign in the numerator if the motion of the detector is toward the source. Use bottom sign in the numerator if the motion of the detector is away the source. v is the speed of sound in the medium vd is the speed of the detector vs is the speed of the source f’ is the frequency detected by the detector moving with speed vd when the source is moving with speed vs. f: is the frequency emitted by the (stationary) source detected by a stationary detector. sign in the denominator if the motion of the source is toward the detector Use bottom sign in the denominator if the motion of the source is away the detector.

How does Al-Khulaifi catch you while speeding?! 17.9 The Doppler Effect: (cont’d) How does Al-Khulaifi catch you while speeding?! Example: A bat, moving at 5 m/s , is chasing a flying insect. If the bat emits a 40.0 kHz chirp and receives back an echo at 40.4 kHz, at what speed is the insect moving toward or away from the bat? (take the speed of sound in air to be v = 340 m/s).

17.9 The Doppler Effect: (cont’d) What if the air( i.e. medium) is moving?!