Physics 1408-002 Principles of Physics Sung-Won Lee [email protected] Lecture 26 – Chapter 16 – April 23, 2009 Announcement I Lecture note is on the web Handout (6 slides/page) http://highenergy.phys.ttu.edu/~slee/1408/ *** Class attendance is strongly encouraged and will be taken randomly. Also it will be used for extra credits. HW Assignment #10 (Ch. 14,15,16) is placed on MateringPHYSICS, and is due by 11:59pm on Wednesday, 4/29 Announcements II Final Exam (All Chapters) 4/30 Thursday @ Sci 7 7:30 am – 10:00 am 2.5 hours Exams - Overview •! The exams are closed book. You may bring one hand-written 3” x 5” index card with formulae, etc. Telephones, iPod and other gizmos are not allowed. Small calculators are allowed. •! The final exam is comprehensive (3~5 min problems) and is a common exam for all sections (~Total 20~25 problems: i.e. 1~2 /chapter) – YES, it’s a multiple choice exam!! •! Please bring a scantron sheet (orange) for the exam!! Announcement III SI session by Reginald Tuvilla Next week, final exam review will be on Monday 04/06 from 4:30 - 7:30. (Room: HH 28) Chapter 16 Sounds •! Characteristics of Sound •! Mathematical Representation of Longitudinal Waves •! Intensity of Sound: Decibels •! Sources of Sound: Vibrating Strings and Air Columns •! Quality of Sound, and Noise; Superposition •! Interference of Sound Waves; Beats •! Doppler Effect & Shock Waves and the Sonic BoomSound can travel through any kind of matter, but not through a vacuum. The speed of sound is different in different materials; in general, it is slowest in gases, faster in liquids, and fastest in solids. The speed depends somewhat on temperature, especially for gases. 16-1 Characteristics of Sound Speed of Sound in Air •! The speed of sound also depends on the temperature of the medium •! This is particularly important with gases •! For air, the relationship between the speed and temperature is –! The 331 m/s is the speed at 0o C –! TC is the air temperature in Celsius Loudness: related to intensity of the sound wave Pitch: related to frequency (High or low) Audible range: about 20 Hz to 20,000 Hz; upper limit decreases with age Ultrasound: above 20,000 Hz; see ultrasonic camera focusing in following example Infrasound: below 20 Hz 16-1 Characteristics of Sound 16-2 Mathematical Representation of Longitudinal Waves Longitudinal waves are often called pressure waves. The displacement is 90° out of phase with the pressure. Longitudinal sound wave traveling to the right, and its graphical representation in terms of pressure Representation of a sound wave in space at a given instant in terms of (a) displacement, and (b) pressure. 16-2 Mathematical Representation of Longitudinal Waves By considering a small cylinder within the fluid, we see that the change in pressure is given by (B is the bulk modulus): Longitudinal wave in a fluid moves to the right. A thin layer of fluid changes in volume as a result of pressure variation as the wave passes. At the moment shown, the pressure will increase as the wave moves to the right, so the thickness of our layer will decrease, by an amount !D. !P = -B(!V/V), !P = -B(S!D/S!x) 16-2 Mathematical Representation of Longitudinal Waves If the displacement is sinusoidal, we have where, using and D = A sin(kx - !t), !P = -!Pmax cos(kx – !t) It is also given by !Pmax = BAk = "v2AkThe intensity of a wave is the energy transported per unit time across a unit area. The human ear can detect sounds with an intensity as low as 10-12 W/m2 and as high as 1 W/m2. [Watts/m2] 16-3 Intensity of Sound: Decibels The loudness of a sound is much more closely related to the logarithm of the intensity. Sound level is measured in decibels (dB) and is defined as: I0 (reference intensity) is taken to be the threshold of hearing: 16-3 Intensity of Sound: Decibels I = the intensity of the sound whose level is to be determined Note: Threshold of pain: I = 1.00 W/m2; # = 120 dB Sound Level, Example •! What is the sound level that corresponds to an intensity of 2.0 x 10-7 W/m2 ? •!# = 10 log (2.0 x 10-7 W/m2 / 1.0 x 10-12 W/m2) = 10 log 2.0 x 105 = 53 dB An increase in sound level of 3 dB, which is a doubling in intensity, is a very small change in loudness. In open areas, the intensity of sound diminishes with distance: However, in enclosed spaces this is complicated by reflections, and if sound travels through air, the higher frequencies get absorbed. 16-3 Intensity of Sound: Decibels Musical instruments produce sounds in various ways—vibrating strings, vibrating membranes, vibrating metal or wood shapes, vibrating air columns. The vibration may be started by plucking, striking, bowing, or blowing. The vibrations are transmitted to the air and then to our ears. 16-4 Sources of Sound: Vibrating Strings and Air Columns 16-4 Sources of Sound: Vibrating Strings and Air Columns This table gives frequencies for the octave beginning with middle C. The equally tempered scale is designed so that music sounds the same regardless of what key it is transposed into.Standing Waves on a String This figure shows the first three standing waves, or harmonics, on a fixed string. Stringed Instruments Waves in a Closed-Closed Pipe A long narrow column of air such as the air in a tube or pipe can support a longitudinal standing sound wave. Such a tube may be “open” or “closed” at each end. A closed end causes a node. An open end causes an antinode. In the example shown here, both ends are closed and the standing wave mode is m=2. There are nodes at each end and one in the center, and there are two antinodes at the quarter wave locations. Example: Singing in the Shower A shower stall is 2.45 m (8 ft) tall. For what frequencies less than 500 Hz can there be vertical standing sound waves in the shower stall? 1(343 m/s)70 Hz2 2(2.45 m)vfL= = =70 Hz, 140 Hz, 210 Hz, 280 Hz, 350 Hz, 420 Hz, and 490 Hz,mf =1, 2, 3, 4, 5, 6, and 7m =, 1, 2, 3, 4,2 / 2mv vf m mL m L= = = !Waves in an Open-Open Pipe n A tube open at both ends (most wind instruments) has pressure nodes, and therefore displacement antinodes, at the ends. Waves in an Open-Closed Pipe only odd harmonics. A tube closed at one end (some organ pipes) has a displacement node (and pressure antinode) at the closed end.Pipes and Modes 112/1, 2,3,4,2mmLmmmvf m mfL! !"= =##=$#= =#%!114/ 1, 3,5,7,4mmLmmmvf m mfL! !"= =##=$#=