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1. a. Derive the following expression for the fractional change in the speed of sound (dv/v) dv 1 dT Start with the expression for the 2 T related to a small change in temperature (dT): - V YRT M speed of sound related to temperature: y = where y is the ratio of heat capacities (a constant), R is the gas constant and M is the molar mass of the substance. Show enough steps (and words!) so that I can tell what you're doing. b. Use the red equation above to determine what the speed of sound in air at 21.0° C is, given that the speed of sound at 20.0° C is 344 m/s. Check your answer against any reference that has the speed of sound in air at different temperatures. Show your setup, and remember that the speed should not be terribly different! Hint: What temperature units should you be using?

1. a. Derive the following expression for the fractional change in the speed of sound (dv/v) dv 1 dT Start with the expression for the 2 T related to a small change in temperature (dT): - V YRT M speed of sound related to temperature: y = where y is the ratio of heat capacities (a constant), R is the gas constant and M is the molar mass of the substance. Show enough steps (and words!) so that I can tell what you're doing. b. Use the red equation above to determine what the speed of sound in air at 21.0° C is, given that the speed of sound at 20.0° C is 344 m/s. Check your answer against any reference that has the speed of sound in air at different temperatures. Show your setup, and remember that the speed should not be terribly different! Hint: What temperature units should you be using?

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1. a. Derive the following expression for the fractional change in the speed of sound (dv/v) dv 1 dT related to a small change in temperature (dT): Start with the expression for the 2 T YRT M speed of sound related to temperature: v= where y is the ratio of heat capacities (a constant), R is the gas constant and M is the molar mass of the substance. Show enough steps (and words!) so that I can tell what you're doing. b. Use the red equation above to determine what the speed of sound in air at 21.0° C is, given that the speed of sound at 20.0° C is 344 m/s. Check your answer against any reference that has the speed of sound in air at different temperatures. Show your setup, and remember that the speed should not be terribly different! Hint: What temperature units should you be using?
Transcribed Image Text:1. a. Derive the following expression for the fractional change in the speed of sound (dv/v) dv 1 dT related to a small change in temperature (dT): Start with the expression for the 2 T YRT M speed of sound related to temperature: v= where y is the ratio of heat capacities (a constant), R is the gas constant and M is the molar mass of the substance. Show enough steps (and words!) so that I can tell what you're doing. b. Use the red equation above to determine what the speed of sound in air at 21.0° C is, given that the speed of sound at 20.0° C is 344 m/s. Check your answer against any reference that has the speed of sound in air at different temperatures. Show your setup, and remember that the speed should not be terribly different! Hint: What temperature units should you be using?
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