Module 8—Mechanical Waves

The Doppler Equation

 

If a sound source is moving towards you (the observer), the wavelength is compressed a distance equal to the amount of distance the source moves during the time it takes to produce one full wave. Considering this fact, and using previous definitions for uniform motion (v = d/t) and period (T = 1/f), the Doppler effect can be described as the following equation:

 

Doppler effect: the observed change in frequency and wavelength of a wave produced by a source moving relative to an observer

     

 

Quantity

Symbol

SI Unit

Doppler frequency (observed)

fd

Hz

source frequency

fs

Hz

wave velocity

vw

m/s

source velocity

vs

m/s

 

When the source is moving towards the stationary observer, the equation produces a higher observed frequency than the source frequency. The equation is as follows:

 

     

 

When the source is moving away from the stationary observers, the equation produces a lower observed frequency than the source frequency. The equation is as follows:

 

     

 

Read

 

How is this formula applied? Read “Analysis of the Doppler Effect” starting from the bottom of page 430 to the bottom of page 432 of your textbook.

 

 Self-Check

 

SC 1. Complete question 1 of “Practice Problems” on page 432 of your textbook.

 

Check your work.
Self-Check Answers

 

SC 1.

 

Given

 

fs = 264 Hz

vs = 60.0 km/h

vw = 340 m/s

 

Required

 

the apparent frequency of the horn (fd)

 

Analysis and Solution

 

Convert the speed of the vehicle to m/s. Use the form of the Doppler effect equation for an approaching vehicle.

 

     

 

Paraphrase

 

The apparent frequency of the horn is 278 Hz.

 

Module 8: Lesson 6 Assignment

 

Remember to submit the answers to TR 4, TR 5, and TR 6 to your teacher as part of your Module 8: Lesson 6 Assignment.

 

Try This

 

TR 4. A fire engine is being driven away from you at a speed of 15.4 m/s. One of the notes in its siren sequence has a fundamental frequency of 244 Hz. If the speed of sound is 338 m/s, what will seem to you to be the fundamental frequency of that particular note?

 

TR 5. An automobile is approaching you at a speed of 50.0 km/h and sounding its horn. The fundamental frequency of the horn sounds to you like 266 Hz. If the speed of sound is 335 m/s, what is the real fundamental frequency of the horn?

 

TR 6. An automobile is approaching you at a speed of 90.0 km/h and sounding its horn. The fundamental frequency of the horn sounds to you like 268 Hz. If the real fundamental frequency of the horn is 248 Hz, what is the speed of sound?