Problem 1.39. By applying Newton's laws to the oscillations of a continuous medium, one can show that the speed of a sound wave is given by B Cs = where p is the density of the medium (mass per unit volume) and B is the bulk modulus, a measure of the medium's stiffness. More precisely, if we imagine applying an increase in pressure AP to a chunk of the material, and this increase results in a (negative) change in volume AV, then B is defined as the change in pressure divided by the magnitude of the fractional change in volume: ΔΡ B = -AV/V* This definition is still ambiguous, however, because I haven't said whether the take place isothermally or adiabatically (or in some other way). compression is
Problem 1.39. By applying Newton's laws to the oscillations of a continuous medium, one can show that the speed of a sound wave is given by B Cs = where p is the density of the medium (mass per unit volume) and B is the bulk modulus, a measure of the medium's stiffness. More precisely, if we imagine applying an increase in pressure AP to a chunk of the material, and this increase results in a (negative) change in volume AV, then B is defined as the change in pressure divided by the magnitude of the fractional change in volume: ΔΡ B = -AV/V* This definition is still ambiguous, however, because I haven't said whether the take place isothermally or adiabatically (or in some other way). compression is
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When Scotland's Battlefield Band played in Utah, one musician remarked that the high altitude threw their bagpipes out of tune. Would you expect altitude to affect the speed of sound (and hence the frequencies of the standing waves in the pipes)? If so, in which direction? If not, why not?
Transcribed Image Text:Problem 1.39. By applying Newton's laws to the oscillations of a continuous
medium, one can show that the speed of a sound wave is given by
B
Cs =
where p is the density of the medium (mass per unit volume) and B is the bulk
modulus, a measure of the medium's stiffness. More precisely, if we imagine
applying an increase in pressure AP to a chunk of the material, and this increase
results in a (negative) change in volume AV, then B is defined as the change in
pressure divided by the magnitude of the fractional change in volume:
ΔΡ
B =
-AV/V*
This definition is still ambiguous, however, because I haven't said whether the
take place isothermally or adiabatically (or in some other way).
compression is
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