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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# Due to efficiency considerations related to its bow wake, the supersonic transport aircraft must maintain a cruising speed that is a constant ratio to the speed of sound (a constant Mach number). If the aircraft flies from warm air into colder air, should it increase or decrease its speed? Explain your answer.

If the aircraft flies from warm air into colder air, its speed should be decreased.

See the step by step solution

## Step 1: dependency of the speed of sound on temperature

Speed of sound increases when the temperature increases as follows

${v}_{w}=331\sqrt{\frac{{T}_{k}}{273}}$

Here ${v}_{w}$ is the speed of a sound wave and ${T}_{k}$ is the temperature in kelvin.

## Step 2: Change in observer’s frequency

The ratio $\frac{{v}_{s}}{{v}_{w}}$ must be constant

here ${v}_{s}$ is the speed of a jet

if temperature decreases then ${v}_{s}$ will also decrease, To maintain a constant ratio $\frac{{v}_{s}}{{v}_{w}}$, ${v}_{s}$ the speed of a jet should also decrease.