Phys 1240 Fa 05, SJP 4-1 (Still a rough draft - I may add some more, but thought I'd get something posted!) This chapter contains some stuff that we won't focus on (like refraction), and the most essential points are a little hidden (namely, the idea of waves "superposing". So I'm going to have us read it in a funny order, starting with 4.1 and 4.5, and then going back to 4.2 (which we'll cover only very loosely), and then 4.3 which is kind of a cool application! 4.4 is fun too, but really not all that important of a point for sound and music, we'll just talk about it briefly (but I'm not going to worry about the formulas there!) The key point from the first section of Chapter 4: remember that sound is a wave, a pressure wave in a medium (usually air). It arises from the steady propagation of a disturbance... It travels with a well-defined speed It travels outwards from sources (in an expanding sphere of influence) Sound will reflect (echo) from hard, flat surfaces. Comments: If the surface is bumpy, sound waves will reflect "every which way" (this is called "diffuse reflection") If the surface is smooth and hard, the sound will reflect much like you would expect billiard balls to reflect off a wall (see Fig 4.1 a in your text) We need to discuss this figure some more, though. What the heck are those *arrows* in Fig 4.1? To explain, first go way back to Fig 1.6a. If you focus on the curved (but mostly "up and down") lines in 1.6a, those are the ones we're used to thinking about to represent sound waves - they look like the "lines of constant high pressure" in that simulation you used for a CAPA homework. The arrows (pointing to the right-ish in that picture) are "rays of sound", they represent the "flow of sound". It's a rather abstract idea, it's NOT something physical! It just shows you how the sound is MOVING...Start at 1.6a, try to mentally visually sound "flowing with the arrows", high pressure fronts following low pressure fronts. (Does that picture make sense?) So now go back to Fig 4.1a, those incoming arrows represent a sound wave which is "heading in towards the wall". We're not showing the pressure at all any more, just the "flow of sound". The arrows just point the way the sound is moving. The sound bounces (echoes) and now it's "heading away from the wall", that's what the outgoing arrows represent. So, what happens depends on the size of the bumps on the wall. But, how bumpy is bumpy? The answer is a little subtle, but basically, it's the wavelength of the sound that determines if it's "smooth" or not. If the bumps are SMALLER than the wavelength of the sound, then the bumps are so small they don't matter, the wall seems smooth. If the bumps are BIGGER than the wavelength of the sound, they're big enough that Fig 4.1b is the more realistic picture. (Why is this? I'm going to leave it as a puzzle for you to mull over for the moment, it's really not so important for where we're heading) Now, remember my favorite Ch. 2 formula: wavelength*frequency = speed, or λ f = 344 m/s (at room temperature, anyway) So, can you see that HIGH frequency sound always has a SMALLER wavelength? E.g, if f=344 Hz, λ =1 meter. That's a "middle pitch" kind of sound, the F right above middle C on a piano. If you go up to 3,444 Hz, then λ = .1 meters (convince yourself!) That's a note from the very high end of the piano keyboard, producing waves 10 times SMALLER in wavelength, about the size of your fist. On the other end of the keyboard, down at about 34 Hz, λ = 10 meters, larger than the piano itself! What this all means is that a wall might be effectively SMOOTH for the low frequency sound hitting it, but at the very same time, in the very same spot, act BUMPY for the higher frequency sound hitting it! This is weird, but true, different sounds (of different frequencies) can behave differently whenPhys 1240 Fa 05, SJP 4-2 striking the same surface. If the wall has bends/angles/bumps that are, say, a few feet in size, then the notes on the HIGH end of the piano keyboard will "notice" them (because the bumps are BIGGER than their wavelength), and bounce at crazy angles. But the notes from the LOW end of the piano will still see a smooth wall (because the bumps are SMALLER than their wavlength) and reflect in a simpler way. When you design rooms for playing music, you have to think about this. There is also absorption at the boundary. Some sound energy will always get absorbed, it doesn't ALL echo perfectly. One way to say this is that the amplitude of the reflected wave going out will be smaller than the amplitude you had coming in. Bigger amplitude <=> louder <=> more energy flowing. Figure 4.2 of the text shows "multiple reflections". When sound is emitted from a source, it heads out in all directions. The sound waves hit walls and floors and ceilings: some energy gets absorbed, but if the walls are fairly smooth and hard, quite a bit of sound will bounce (echo, reflect). So there are LOTS of possible paths for sound waves to travel, they bounce and bounce and reflect around. Think of pinballs in a pinball machine, bouncing all around. (Ouch - now I'm asking you to think of sound as THINGS, pinballs?! Is that a bad idea? Sound is a wave, not a pinball! But it's ok, sometimes it's not the worst mental image in the world to think about. That's what those "rays" or arrows in the figures are leading ME to think about, I guess...) Multiple reflection is ONE (of two) main reason why you can hear sounds from other rooms, even if there's no "line of sight" from you to the source. Even if light cannot go straight from source to you, the sound can bounce around a little and reach you through a slightly more complicated path. (Look at fig 4.2 again!) Sound travels so darn fast (344 meters in one second) that the slight delay from having to bounce a few times and take a longer path is not noticeable in ordinary sized areas or ordinary circumstances. There is ANOTHER way that sound can get to you (by BENDING around corners!) that is quite different, (diffraction) which is the subject of section 4.2. We'll come back to it shortly. The text talks about refraction next, yet another kind of "bending" of sound paths - feel free to look it over, but it's just not all that important a physical effect for sound or music in most circumstances, I'm not going to talk about it. I want to skip right to the heart of this chapter, section 4.5. This talks about INTERFERENCE of
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