11.3. Resonance with Sound Waves http://www.ck12.org
FIGURE 11.15
FIGURE 11.16
An old crystal radio set.another pendulum of the same length. So when tuned, only a specific radio frequency will cause resonance in the
radio antenna.
Strings Fixed at Both Ends
A case of natural frequency that you can observe plainly is when you pluck a string or stretched rubber band. Nor-
mally, the string will vibrate at a single widest point in the middle. This is called the fundamental or first harmonic
resonance of the string. This is the same as the natural frequency of a simple pendulum or mass on a spring. Because
it vibrates all along its length, though, the string also lets us see further patterns of resonance.
By vibrating the end of the string rather than just plucking it, we can force vibration at frequencies other than the
first harmonic. When the string is set into vibration, energy will travel down the string and reflect back toward the
end where the waves are being generated. This steady pattern of vibration is called a standing wave.The points
where the reflecting waves interfere destructively with the “generated’ waves are called nodes. The points where the
reflecting waves interfere constructively with the generated waves are called anti-nodes.
Figure11.17 shows a string fixed at both ends vibrating in its fundamental mode. There are two nodes shown and
one antinode. The dashed segment represents the reflected wave.