©1997 by Eric Mazur Published by Pearson Prentice Hall Upper Saddle River, NJ 07458 ISBN 0-13-565441-6 No portion of the file may be distributed, transmitted in any form, or included in other documents without express written permission from the publisher.
Sound
The four figures below represent sound waves emitted by moving source The four figures below represent sound waves emitted by moving source. Which picture(s) represent(s) a source moving at less than the speed of sound? Answer: A and C. In figure B, (see following figure) the wavefront created when the source was at the center of circle 1 has traveled the distance between lines 1 and 3. Similarly, the wavefront created when the source was at the center of circle 2 has traveled the distance between lines 2 and 3. This means that the source had to move at exactly the speed of the sound waves—else the wave emitted at 2 would not catch up with that emitted at 1.The result of this motion at the speed of sound is a piling up of sound waves in front of the source at 3. In figure D, the wavefronts emitted later have moved beyond those emitted earlier, indicating that the source moves faster than the speed of sound. In figure A, all the wavefronts are concentric, indicating that the source is stationary. Figure C shows a moving source of sound, but the displacement of the wavefronts is less than in B so the source is moving at a speed slower than the speed of sound.
Explanation Answer: A and C. In figure B, (see following figure) the wavefront created when the source was at the center of circle 1 has traveled the distance between lines 1 and 3. Similarly, the wavefront created when the source was at the center of circle 2 has traveled the distance between lines 2 and 3. This means that the source had to move at exactly the speed of the sound waves—else the wave emitted at 2 would not catch up with that emitted at 1.The result of this motion at the speed of sound is a piling up of sound waves in front of the source at 3. In figure D, the wavefronts emitted later have moved beyond those emitted earlier, indicating that the source moves faster than the speed of sound. In figure A, all the wavefronts are concentric, indicating that the source is stationary. Figure C shows a moving source of sound, but the displacement of the wavefronts is less than in B so the source is moving at a speed slower than the speed of sound.
observers. Which of the following is true? Three observers, A,B, and C are listening to a moving source of sound. The diagram below shows the location of the wavecrests of the moving source with respect to the three observers. Which of the following is true? 1. The wavefronts move faster at A than at B and C. 2. The wavefronts move faster at C than at A and B. 3. The frequency of the sound is highest at A. 4. The frequency of the sound is highest at B. 5. The frequency of the sound is highest at C. Answer: 5.The speed at which the wavefronts move is the speed of sound in air, which is independent of the speed of the source and the location of the observers. So the first two choices are incorrect. The observed frequency, however, is determined by the number of wavefronts passing the observer per unit time. So, the more closely the wavefronts are spaced, the higher the frequency. Inspection of the figure shows that the wavefronts are most closely spaced for observer C.
1. a sonic boom only when the airplane breaks the sound The following figure shows the wavefronts generated by an airplane flying past an observer A at a speed greater than that of sound. After the airplane has passed, the observer reports hearing 1. a sonic boom only when the airplane breaks the sound barrier, then nothing. 2. a succession of sonic booms. 3. a sonic boom, then silence. 4. first nothing, then a sonic boom, then the sound of engines. 5. no sonic boom because the airplane flew faster than sound all along. Answer: 4. The observer first hears nothing because the sound waves haven’t reached the location of the observer yet. When the wake caused by the sound waves reaches the observer, a sonic boom is caused by the overlapping crests of the sound waves. After this, the sound of the engines is heard, as indicated by the regularly spaced sound waves inside the wake.