Standing Waves

210 the speed of sound the speed of any mechanical

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Unformatted text preview: ar. 2.10 The Speed of Sound The speed of any mechanical wave, transverse or longitudinal, depends on both an inertial property of the medium (to store kinetic energy) and an elastic property of the medium (to store potential energy). Thus, we can generalize equation (31) which gives the speed of a transverse wave along a stretched string, by writing elastic property inertial property (32) where (for transverse waves) τ is the tension of the string and μ is the string’s linear density. If the medium is air, and the wave is longitudinal, we can guess that the inertial property, corresponding to μ, is the volume density ρ of air. What shall we put as the elastic property? In a stretched string, potential energy is associated with the periodic stretching of the string elements as the wave passes through them. As a sound wave passes through air, potential energy is associated with periodic compressions and expansions of small volume elements of the air. The property that determines the extent to which an element of a medium changes in volume when the pressure (force per unit area) on it changes is the bulk modulus B defined as ∆ ∆⁄ (33) Here ΔV/V is the fractional change in volume produced by a change in pressure Δp. From Equation (33), we see that the unit for B is the Pascal. The signs of Δp and ΔV are always opposite: When we increase the pressure on an element (Δp is positive), its volume decreases (ΔV is negative). We include a minus sing in Equation (33), so that B is always a positive quantity. Now substituting B for τ and ρ for μ in equation (32) yields (34) as the speed of sound in a medium with bulk modulus B and density ρ. 3.0 References • • • Fundamentals of Physics Extended 7th edition by Halliday Resnick and Walker. Wiley Publishing. Physics for Scientists and Engineers: A Strategic approach with Modern Physics by Randall D. Knight. Addison Wesley Publishing Essentials of College Physics by Serway and Vuille. Brookscole Publishing. 9 4.0 The Experiment 4.1 Standing Waves in a String The first part of the experiment that you will do today, is find the frequency, wavelength, and velocity of the waves on the string. The first that must be done is to weight the string that you will be using. This is given by m and will me measured in kg. Next, you will measure its length L in m. Using these to pieces of information, you will be able to find the linear density by using (35) where ms is the mass of the string. Next, you will hang a mass at the end of the string. Make sure that you record the mass in kg. Now that we have a hanging mass on the string, we must also take into accou...
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This document was uploaded on 03/20/2014 for the course PHYS 215 at Lafayette.

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