Physics 116 Lecture 6 Sound Oct 7, 2011 R. J. Wilkes Email: - PowerPoint PPT Presentation

Physics 116 Lecture 6 Sound Oct 7, 2011 R. J. Wilkes Email: ph116@u.washington.edu

Announcements • � Guest lecturer today: Michael Dziomba • � Wilkes will be back at 2:45 today, for office hour (until 3:15)

Lecture Schedule (up to exam 1) Today 10/7/11 Physics 116 - Au11 3

Waves on strings • � End effects: – � If end of rope is fixed in wall and can’t move, • � reaction force from wall (Newton’s 3 rd Law) opposes motion: upward pulse coming toward wall becomes downward pulse leaving wall • � Pulse is inverted – � If end of rope is unconstrained and can move vertically, • � no reaction force • � pulse is reflected without inversion • � Wave speed on a rope or string depends on – � Tension in string : if F=0 wave does not propagate – � Mass of string : really, mass per unit length • � Speed of wave on a string Justify this result with dimensional analysis: 10/7/11 Physics 116 - Au11 4 4

Example • � Rope has 92 N tension and is 12 m long • � Pulse takes 0.45 s to travel length of rope • � What is total mass of rope? 10/7/11 Physics 116 - Au11 5 5

Space and time pictures of waves Last time: We’ve been through this already with oscillations… • � We could stand at one place and watch wave move past us vs time • � Graph of displacement vs time • � Period T = time for one cycle ("wavelength" in time units) to go past • � Frequency f = cycles passing per second (hertz, Hz) = 1/T – � This wave has 1 cycle in 1 s, so T = 1 s – � Amplitude is 2 meters T= 1 s variation with time at a fixed point in space A = 2 m time, seconds (Here: period T=1sec) 10/7/11 Physics 116 - Au11 6

At one instant: a snapshot in time Last time: • � Previous picture was graph of displacement vs time at one location • � Here: Picture of rope at one instant of time (say, t=0): – � We see rope’s displacement vs position along rope (y vs x) Wavelength ! = length of one full cycle (distance between peaks) • � • � Amplitude A = maximum displacement (height) ! = 1 m snapshot = picture of rope, frozen at one instant of time: A = 2 m configuration in space at a fixed point in time (Here: wavelength ! =1 m) 10/7/11 Physics 116 - Au11 7

Harmonic functions to describe wave motion • � To describe waves, we need to give {disturbance} = y (x, t) • � From our “snapshot” plot we see • � From our “standing in one place” plot, we see that the position of the peak that was at x=0 at t=0, has moved to the right after time t, by a distance • � So the value of the wave function at time t is equal to the value at time t=0 for any combination of x and t such that x � t T � = 0 • � So we can describe the wave with the “harmonic function” * * The circular functions sin/cos are “harmonic” because they can describe sound waves that are multiples of some base frequency – next time… 10/7/11 Physics 116 - Au11 8 8

Example A transverse wave has ! = 2.6 m, and moves in the + x direction • � (“to the right”) with speed 14.3 m/s • � Its amplitude is 0.11 m and it has y=0.11 m at t=0 • � Give an equation describing y(x,t) for this wave General form for a wave moving in +x direction* is (for y=A at t=0 *) For this wave, So * What if it were moving to the left (-x)? what if it had y=0 at t=0, with y increasing at that time? what if it had y= -1 at t=0, with y increasing? 10/7/11 Physics 116 - Au11 9 9

Sound waves Last time: • � Sound waves are an example of longitudinal waves – � Disturbance consists of periodic changes in density of the medium – � At any point, material is alternately compressed and rarified – � Compression peaks propagate through the medium • � Sound = compression wave in material medium (air, water, iron) www.kettering.edu/~drussell/Demos/waves/wavemotion.html • � Sound speed depends on material properties and density (so, temperature, humidity etc) 10/7/11 Physics 116 - Au11 10

Speed of sound • � Speed of sound c is about 343 m/s in air (depends on air density, temperature and humidity) = 1235 km/hr = 770 mph – � So sound travels 1 mile in about 5 sec (lightning and thunder) At 0°C, c = 331 m/s At 15°C, c = 340 m/s At 20°C, c = 343 m/s At 25°C, c = 346 m/s • � Speed is faster in denser materials: • � Example: Pirate sees cannon on pursuing ship flash, and counts 8 seconds before he hears the boom – how far away is the Royal Navy? 10/7/11 Physics 116 - Au11 11 11

Sound frequency; pitch and musical tones • � Frequency ranges – � Audible – nominally 20 Hz to 20 kHz (actual range is closer to 50Hz-15kHz) – � Infrasonic - below audible (below about 0.1 Hz we call it “vibration” !) – � Ultrasonic - Above 20 kHz • � Speed of sound does not vary much with f – � If v depended on f, sound signals would change significantly depending upon how far away you are • � This is called “dispersion” – � Small f dependence can be observed, for example in undersea sound transmission • � A pulse with many frequencies in it will spread out in time as it travels • � Pitch will vary – pulse becomes a “chirp” • � Perception of sound – � Pitch = perceived frequency of sound – � Associated with musical tones by our brain – � JND = “just noticeable difference” in frequency ~0.4 Hz – � Harmonic scales: eg in western music, “A above middle C” = 440 Hz, next A (one octave higher pitch) = 880 Hz - octave = doubling of base frequency) – � “Equal temperament” scale: 12 tones per octave, each is 1.06 f of previous 10/7/11 Physics 116 - Au11 12 12 (factor = 12 th root of 2)