Chapter 16, Problem 29P

### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278

Chapter
Section

### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278
Textbook Problem

# The speed of sound in air (in meters per second) depends on temperature according to the approximate expression v = 331.5 + 0.607 T C where TC is the Celsius temperature. In dry air, the temperature decreases about 1°C for every 150-m rise in altitude. (a) Assume this change is constant up to an altitude of 9 000 m. What time interval is required for the sound from an airplane flying at 9 000 m to reach the ground on a day when the ground temperature is 30°C? (b) What If? Compare your answer with the time interval required if the air were uniformly at 30°C. Which time interval is longer?

(a)

To determine

The required time interval for the sound to reach the ground when the ground temperature is 30.0°C.

Explanation

The altitude of the plane is 9000â€‰m, the temperature at the ground is 30.0Â°C, the temperature in dry decreases about 1Â°C for every 150â€‰m rise.

The speed of the sound at an altitude of 9000â€‰m from the ground is,

Â Â Â Â vâ€²=331.5âˆ’0.607TC

Substitute 30.0Â°C for TC in above expression.

Â Â Â Â vâ€²=331.5âˆ’0.607(30.0Â°C)=313.29â€‰m/s

The expression for the velocity at the ground is given as,

Â Â Â Â v=331.5+0.607TC

Here, TC is the temperature in Celsius.

Substitute 30.0Â°C for TC in above expression.

Â Â Â Â v=331.5+0.607(30.0Â°C)=349.71â€‰m/s

Formula to calculate the average speed of the sound is,

Â Â Â Â vavg=v+vâ€²2

Substitute 349

(b)

To determine

The time interval required if the air were uniformly at 30.0°C and compare it with the time interval calculated in part (a).

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