## Beat Frequency

Two automobiles are equipped with the same single-frequency horn. When one is at rest and the other is moving toward an observer at 16.9 m/s, a beat frequency of 5.49 Hz is heard. What is the frequency the horns emit? Assume T = 20°C .

**106 Hz****Approach**

The beat frequency is the difference in two frequencies, generally two that are closed to each other. The frequency heard by the observer from the stationary automobile is unchanged. However, the frequency heard by the observer from the moving automobile will be higher since the automobile is moving towards the observer.

## **Solution**

Given quantities:

f obs = fo/(1-vsource/vsound)

The beat frequency:

fbeat = [fo/(1-vsource/vsound) ]-fo

Solving Gives

fo=fbeat((vsound/vsource)-1)

Plug and chug to get fo=106 Hz

- Beat frequency, fbeat = 5.49 Hz
- Speed of one automobile, vsource = 16.9 m/s

f obs = fo/(1-vsource/vsound)

The beat frequency:

fbeat = [fo/(1-vsource/vsound) ]-fo

Solving Gives

fo=fbeat((vsound/vsource)-1)

Plug and chug to get fo=106 Hz