Concept explainers
(a)
To calculate:
Calculate the derivative of speed of the sound in air as respect to absolute temperature.
(a)
Answer to Problem 34P
Derivative of the speed of the sound in air as respect to absolute temperature is
Explanation of Solution
Given:
Differentials
Formula used:
Calculation:
The speed of sound in a gas is given by
Where,
To estimate the percentage change in the speed of sound if the temperature increases from
For evaluating the
Now, to separate the variables to obtain,
Conclusion:
Derivative of the speed of the sound in air as respect to absolute temperature is
(b)
To calculate:
The percentage change in speed of the sound when temperature changes from
(b)
Answer to Problem 34P
The percentage change in speed of the sound when temperature changes from
Explanation of Solution
Given:
Differentials
Temperature
Temperature
Formula used:
Calculation:
The given equation is:
First differentiate the expression with respect to
To estimate the percentage change in the speed of sound if the temperature increases from
Approximate the
Put the numerical values to get,
Conclusion:
Thus, the percentage change in speed of the sound when temperature changes from
(c)
To calculate:
Calculate the value at
(c)
Answer to Problem 34P
The value at
Explanation of Solution
Given:
Speed of the sound
Temperature
Formula used:
Calculation:
According to the question,
Using the differential approximation, approximate the speed of sound at
Now, put the numerical values and evaluate the
Conclusion:
Thus, the value at
(d)
To explain:
Calculate an approximation comparison with result of an exact calculation.
(d)
Answer to Problem 34P
Approximation comparison with result of an exact calculation
Explanation of Solution
Given:
Speed of the sound
Temperature
Formula used:
The speed of sound wave at the absolute temperature is:
Here,
- Molecular mass of hydrogen:
Constant (hydrogen is diatomic gas):
Absolute temperature:
Gas constant:
Calculation:
The speed of sound wave at the temperature
The speed of sound wave at the temperature
Now, divide the first of these equations by the second and solve for
And,
Conclusion:
Approximation comparison with result of an exact calculation
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Chapter 15 Solutions
PHYSICS F/SCIEN.+ENGRS. W/SAPLING >IC<
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