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CU-Boulder PHYS 1240 - Pressure sound and waves

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1Physics 1240: Sound and Music 2/2/06 Today: Pressure sound and waves Next Time: Interference and beats, sound intensity Outline Sound sources (string, reed, brass, voice, flute-type) Resonance (vibrations) Nature of sound waves Last time: Pressure atmospheric pressure sound waves are pressure fluctuations Wave motion transverse versus longitudinal waves frequency and wavelength superposition reflection Sound Waves Air is what is called a compressible fluid. It is spongy, you can smash it, then let it expand back. If you push on it, it decreases in volume. For example, when you pump air into your bicycle tire, air reduces in volume and increases in pressure. Alternately, if it is allowed to expand it will. E.g. when a balloon expands when connected to a high pressure source. Sound waves are small compressions and expansions (rarefactions) of air. Convincing you that sound is simply pressure disturbances propagating from a source to the listener will not be easy. 1) We cannot see the air around us, that is, the medium of sound waves. If we can't see the medium how are we going to see the waves which propagate within it? 2) Sound produces pressure fluctuations that are one-millionth of the background of the air pressure. What is pressure anyway? Pressure2Pressure is the amount of force applied per unit area. p = F / A Newtons/m2 or Pascals (Pa). Background air pressure is 105 N/ m2. The background air pressure is a lot. We are buried beneath a sea of air, the earth's atmosphere. Why is the background air pressure so huge? Well, you can think of earth as a giant spherical fish tank, and we have a 50 km or so of air on top of us pressing down. Air weighs something. A lot less than water, but the atmosphere is pretty high, so it weighs a lot! I've drawn a 1m x 1m square on the board for perspective. 4.5 N= 1 lb (you do not need to know this specific fact). If we took a 100,000 N weight (22,000 lb) and spread it uniformly of the 1m x 1m surface (say put it on a VERY STRONG piece of plywood). This would be 105 N/ m2, or equivalent to atmospheric pressure. This is a heck of a lot of weight or force, and pressure! A 1000 N person (220 lbs) standing on this square piece of plywood would only exert 1000 N/m2! Or, only 1% of atmospheric air pressure! It is important to understand that in p=F/A, the area plays an equal role. A woman can do a lot of damage to hardwood floor when wearing heels with a very small surface area, e.g. 2 cm2 (0.0002m2). Your eardrum is very small (0.3cm), so very small forces are involved in hearing (nature has miniaturized your ear's components to save space for other important things). Sound waves of musical interest have an amplitude of 0.01 to 1 N/ m2. That is the pressure fluctuates between say: 100,000 + 1 N/m2 to 100,000 -1 N/m2 We will talk more about the amplitude, intensity and level of sound waves, in a later chapter. However, this is a very small change in pressure. How many percent would this be? 0.001 % And, this would be for a loud sound! This is one of the reasons it is hard to observe sound waves directly.3Wave Motion One important aspect of physical nature (or physics) is the similarities or strong analogies between vastly different phenomena. Wave motion is such an example. Sound waves, water waves, radio waves, light waves, they all follow very similar patterns and rules. Slinky waves We study waves on a coiled spring because we can more clearly see what is going on. The longitudinal (or compressional) waves we generate here, are very similar to sound waves. The pulse moves at a fixed speed (what we call propagates). A good way to understand sound waves is to examine wave phenomena in other mediums. We know that wave motion is a generic physical phenomenon and we can take what we learn from observing waves we can actually see and apply it to sound. Of course, you should be skeptical and ask "Why should we expect waves on the ocean to behave like sound waves?" Well, physicists have learned that waves of various types have common properties. But, more importantly, we can do various experiments with sound waves, and gradually begin to trust that "Yes, sound does behave like a water wave in this context." When using wave analogs you need to keep in mind both the similarities AND the differences between various types of waves. For example, there are two types of waves: Transverse Waves waves on a string, water waves, electromagnetic waves Motion of the medium is perpendicular to the direction the wave propagates. Longitudinal Waves Sound waves, some seismic waves, waves on a spring Motion of the medium is in the direction of wave propagation. For all mechanical waves, we have a "medium" which moves back and forth slightly, and a wave, which carries information, and energy, which moves great distances (relative to the motion of the medium). The wavelength is the distance it takes for the wave to repeat itself. Look at a snapshot in time of the wave (keep time fixed). The period is the time it takes the wave to repeat itself. Look at a fixed location and plot the wave motion versus time (keep position fixed). frequency = 1 / period (as before and always) The wave speed is how fast the wave is propagating (or moving).4 frequency = speed / wavelength Why? Take a fixed wave shape and move past a fixed point with a fixed speed, you will then see an oscillation that has a frequency corresponding with this formula. I will demonstrate the following in class: using that vinyl hose tied up there. This is a wave pulse. Sound waves (under most situations) have a wave speed that is independent of the amplitude of the wave and the frequency. If the wave speed depends on amplitude we call it a nonlinear wave. If the wave speed depends on frequency, then we have a dispersive wave. Nonlinearities and dispersion are important features in determining timbre. For example, the effect of finite string stiffness causes wave dispersion and this is critical in determining the way a piano sounds. Dispersion is easy to handle mathematically. Nonlinearities are usually very hard to model (shock fronts, chaos, turbulence, etc.). Superposition Another important property of linear waves is “the principle of linear superposition” which is simply the following: when two waves cross paths their displacements add. This is shown below in the figure. It does not matter what the pulse shapes are or how


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CU-Boulder PHYS 1240 - Pressure sound and waves

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