http://www.ck12.org Chapter 11. Vibrations and Sound
Answer:The absolute value of their difference 4. 0 cm− 3. 0 cmor| 3. 0 cm− 4. 0 cm|= 1. 0 cm
- The difference in path length between the two speakers of a stereo system is 2.0 m with respect to the listener.
Will the listener hear two f-notes of wavelength 0.98 m undergo constructive or destructive interference?
Answer:Correctly employing significant digits, we find that two complete wavelengths of an f-note will fit into the
path difference. So the f-notes undergo complete constructive interference.
path di f f erence
wavelength=
2. 0 m
0. 98 m= 2. 04 → 2. 0 wavelengthsBeats
Another result of wave interference is the phenomenon of beats. When two sound waves have frequencies very
close to each other we can hear a “wobbling” sound of the vibrations of the waves, as represented inFigure11.5.
The maximum amplitude of the “green wave” (or envelope) corresponds to the maximum sound of the wobble.
Essentially, some segments of each wave interfere constructively while others interfere destructively. The wobbling
sound mentioned above is louder as the waves interfere constructively. Conversely, the sound is softer as the
waves interfere destructively. The frequency with which the sound alternately increases and decreases its volume
is calledthe beat frequency.When tuning forks of frequencies 261 Hz and of 268 Hz are struck, you will hear the
characteristic beat frequency. If you have ever listened to someone tune a guitar by striking one string and slowly
changing the tension in another string, you may have heard a beat frequency when the two strings were nearly tuned.
In fact, hearing the beat frequency is a sign that the tuning is proceeding correctly!
FIGURE 11.5
The beat frequency is found by subtraction: fbeat=f 2 −f 1 →In the example of the two tuning forks above, the