Chapter 25, Problem 21A

A fire engine’s siren emits a certain frequency. Rank from greatest to least the apparent frequency heard by the stationary listener in each scenario.

(A) The fire engine is traveling toward a listener at 30 m/s.

(B) The fire engine is traveling away from a listener at 5 m/s.

(C) The fire engine is traveling toward a listener at 5 m/s.

(D) The fire engine is traveling away from a listener at 30 m/s.

To determine

To rank: The apparent frequency heard by a stationary listener from greatest to least.

Answer to Problem 21A

A>C>B>D

Explanation of Solution

Introduction:

According to the Doppler Effect, when a source moving towards the stationary observer, the apparent frequency heard by the listener increases.

When the fire engine is moving towards the stationary listener with greater speed, then the listener will hear a louder noise. But, when it is moving away with the same greater speed, then the listener will hear a very faded noise.

When a fire engine traveling towards a stationary listener with $30\text{ m/s}$ , he will hear a louder noise as compared to when a fire engine traveling towards the listener with $\text{5 m/s}$ .

When a fire engine traveling away from a stationary listener with $\text{5 m/s}$ , he will hear a faded noise but louder as compared to the when a fire engine traveling away from the listener with $30\text{ m/s}$ .

Conclusion:

Thus, ranking from greatest to least apparent frequency heard by a stationary listener is A>C>B>D.