Musical Acoustics Lecture #3 - PowerPoint Presentation

1. Musical Acoustics Lecture #3Last time:Sound waves reflect off impedance mismatches. Reflecting off a higher impedance gives a non-inverted pressureReflecting off a lower impedance gives an inverted pressure[We didn’t discuss it, but reflection of a displacement pulse off a higher impedance is inverted, just like for the wave table or rubber rope. Reflection of a displacement pulse off a lower impedance is not inverted, again, just like a pulse on the wave table or rubber rope. Displacement and pressure waves are “out of phase”, and that accounts for the difference.]There is a worksheet due on Thursday, posted.Office Hours (in Regener 111)?

2. Wave phenomenologyAny object moving at speed c will go a distance c.t in time t.Example: Traveling 4 s at 5 m/s you will go 20 m. (Using units can help you check your formulas!)The time for the wave to move so that crest A is where crest B is (now) is called the period of the wave, t. (tau)So c.t = l where c is the wave speed.If you stay in one place and watch crests go by, you will see 1/t crests per unit time. This is the frequency, f.A BNote: for sound, the y-axis is the deviation of pressure from ambient.

3. Wave phenomenologyc . t = l Using f= 1/t you get f . l =c.The speed of sound in air is about 343 m/s. What is the wavelength of a 343 Hz = 343 cycles/s tone?1 m1/343 m3432 mA BAnswer aWe can measure how big a sound wave is by the “amplitude” = the maximum pressure deviation from ambient

4. For audible sounds in air, the speed of sound is independent of frequency.TrueFalseTrue. If this were not true, it would be impossible to listen to a marching band at a football game… the flutes and the tubas would be out of synch!

5. How “big” a sound wave is can be specified by the pressure amplitude.But (and this is important) the energy and power (per unit area) in any wave scales with the amplitude squared. (Power per unit area is called intensity.)When sound travels down a pipe, it carries energy. The energy is almost entirely conserved (a tiny tiny bit is lost to heating of the pipe.) So the amplitude of the sound wave doesn’t change.But if sound spreads out in space, it must get weaker the farther it goes… because energy is conserved. The same energy per unit time (power) flows through an imaginary sphere with any radius around the source. The surface area of a sphere is 4pr2. Conservation of energy requiresI. 4pr2 = constant. So I ≈ constant/r2.Suppose you have a surface (2D) wave, like in the Ripple simulation.How will the wave intensity depend on distance from the source?

6. Humans being human beings, what we perceive as “loudness” is neither the amplitude nor the power in a sound wave. Humans will say a sound is twice as loud as another if the intensity is ten times as large!If you want to lower the intensity of sound by four-fold, you move to twice the distance... But if you want to lower the loudness by four-fold (i.e. Make the sound ¼ as loud), you need to bring the intensity down by factor of 100! You need to get 10 times as far away.Let’s put some of this on the board, so we don’t have to keep it in our heads!Amplitude falls like 1/rIntensity falls like 1/r210-fold change in intensity = 2-fold change in loudness

7. Some practice:If you go 3 times as far from a source of sound, how does the intensity of the wave change (if it spreads in 3D)?It gets bigger by 3-fold (it’s 3 times as big.)It gets smaller by 3-fold (it’s 1/3 as big.)It gets smaller by 9-foldAnswer c. I≈1/r2. The amplitude will decrease by only a factor of 3. The loudness of the sound will be decreasedby about a factor of 2by exactly a factor of 3by exactly a factor of 9by about a factor of 10Answer a. Perceived loudness is cut in half if the intensity is decreased by a factor of 10. Which is close to 9.

8. We already saw that a wave can reflect off a hard surface, namely the wall at the end of a tube.Waves will reflect off any interface with a different impedance. For a nice, smooth, flat surface, the angle of incidence = angle of reflection.Notice how the incoming and outgoing waves are “mirror images”… it’s no accident we call flat, reflecting surfaces “mirrors”!Incoming OutgoingReflecting Surface

9. What if the surface isn’t flat?A smooth, curved surface can focus a wave.RippleSetup Parabolic MirrorResolution ~ 360Move probeSource Freq 15Suppose I wanted to study one wavefront, rather than a sine wave?You can turn off the source at any time.

10. What if the surface is ROUGH?What does “rough” mean?When surfaces are rough (compared with a wavelength), the reflected wave goes willy-nilly! With light, we call such a surface “matte”. (It’s not shiny.)To be a good mirror, a reflective surface only has to be smooth compared with the wavelength. Optical mirrors are not “atomically smooth.”

11. A misleading physics term – INTERFERENCESound waves (and most waves) go right through each other!When two waves are present in the same place and time, their pressure deviations add (taking into account the signs of the deviations!)So it’s kind of silly to say that two waves interfere with each other!1. Ripple demonstration of two sources. The pattern of loud and quiet regions is called an “interference pattern.” Why are some places loud?2. Two sources, with real sound. Let’s measure the wavelength of this sound. (We need string and a ruler.)

12. Refraction & DiffractionFirst: The Huygens Wavelet idea:Every point on the wave “crest”(where pressure is high) acts like a sourceEach of these point sources sends its wave mostly forward.Which one is the world-renowned physicist?

13. Refraction – Wave bending (change in direction) caused by speed differencesWaves bend toward the slower medium.The speed of the wave in the blue medium isSlowerFasterThe same asthe speed in the black medium.Refraction (and Reflection, of course!) in Ripple

14. Refraction doesn’t require a sharp interface… just differences in wave speed. Similar to sound, light travels faster through hotter air. Is the air near the highway hotter or colder than the air a few feet up?Mirage

15. In water, higher pressure makes sound go faster, but colder water makes it go slower. As you go lower in the ocean, you reach a depth where the speed of sound is a minimum. Sound waves at this depth can be trapped by refraction. So they only spread out in 2D. That means their Intensity falls like 1/r… much slower than 1/r2.Whales use this channel to communicate![A similar layer exists in the atmosphere at about 100,000 ft. That’s actually where the air is coldest. Space aliens use the atmospheric layer to communicate.]