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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.
• Fundamentals of Physics Extended 7th edition by Halliday Resnick and Walker. Wiley
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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- Fall '09