Solution Found!
Unless indicated otherwise,
Chapter 16, Problem 10E(choose chapter or problem)
Unless indicated otherwise, assume the speed of sound in air to be \(v=344 \mathrm{~m} / \mathrm{s}\).
CALC (a) Show that the fractional change in the speed of sound \((d v / v)\) due to a very small temperature change \(d T\) is given by \(d v / v=\frac{1}{2} d T / T\). (Hint: Start with Eq. 16.10.) (b) The speed of sound in air at \(20^{\circ} \mathrm{C}\) is found to be \(344 \mathrm{~m} / \mathrm{s}\). Use the result in part(a) to find the change in the speed of sound for a \(1.0^{\circ} \mathrm{C}\) change in air temperature.
Equation Transcription:
Text Transcription:
v=344 m/s
(dv/v)
dT
dv/v=1/2dT/T
20degC
344 m/s
1.0degC
Questions & Answers
QUESTION:
Unless indicated otherwise, assume the speed of sound in air to be \(v=344 \mathrm{~m} / \mathrm{s}\).
CALC (a) Show that the fractional change in the speed of sound \((d v / v)\) due to a very small temperature change \(d T\) is given by \(d v / v=\frac{1}{2} d T / T\). (Hint: Start with Eq. 16.10.) (b) The speed of sound in air at \(20^{\circ} \mathrm{C}\) is found to be \(344 \mathrm{~m} / \mathrm{s}\). Use the result in part(a) to find the change in the speed of sound for a \(1.0^{\circ} \mathrm{C}\) change in air temperature.
Equation Transcription:
Text Transcription:
v=344 m/s
(dv/v)
dT
dv/v=1/2dT/T
20degC
344 m/s
1.0degC
ANSWER:
Solution 10E
Step 1
The Eq. (16.10) is given by
…………(1)
Differentiating the above equation with respect to , we have
………….(2)
Now dividing equation (2) with respect to equation (1) we have
………………..(3) (proved)