Physics principles and equations

The equation for sound level with respect to the power of the sound source is

Mathematics principles

log (a)í log (b) = log (a/b)

Step-by-step solution

To increase the sound level by 10 decibels, the sound power (and sound intensity) must increase tenfold. Raising the maximum sound intensity

of the system by 20 decibels requires a 100-fold increase in sound power and stereo power. The result will be loud enough to ensure the entire

dormitory hears your music!

We hope they appreciate your taste.

Step Reason

1. sound level power equation

2. current system

3. proposed system

4. subtract

5. difference of logarithms

6. divide and simplify

7. take antilogarithm

8. P 2 = 1000 W solve

16.7 - Doppler effect: moving sound source

Doppler effect: A change in the frequency of a

wave due to motion of the source and/or the

listener.

You experience the Doppler effect when a train races past you while sounding its

whistle. As the train is approaching, you perceive the whistle as emitting sound of one

frequency, and as it moves away, the perceived frequency of the whistle drops to a

lower pitch.

This effect is named for the Austrian physicist who first analyzed it, Christian Doppler

(1803-1853). Doppler’s research concerned light from stars, but his principles apply to

sound also.

In the example described above, the frequency of the sound emitted by the train is

constant. The Doppler effect occurs because of the motion of the source of the sound, the train whistle. It is moving first toward and then away

from you, and you are standing still. (What is moving and what is still is relative to sound’s medium, the air.)

You see this situation illustrated on the right. In Concept 1, the train and listener are both stationary. The diagram shows the peaks of the

sound waves as they emanate from the train and radiate in all directions, including toward the listener. They are equally spaced, which means

their wavelength is constant, as is their frequency.

In Concept 2, the train is moving to the right, toward the listener, at a source velocity vs. As you see, the peaks of the sound waves at the

listener are closer together than in Concept 1, which means the wavelength is shorter and the frequency at the listener is higher.

Sound source stationary

Wavelength, frequency constant

(^314) Copyright Kinetic Books Co. 2000-2007 Chapter 16