11.3. Resonance with Sound Waves http://www.ck12.org
11.3 Resonance with Sound Waves
Objectives
The student will:
- Understand the conditions for resonance.
- Solve problems with strings and pipes using the condition for resonance.
Vocabulary
- beat frequency
- natural frequency:The frequency at which a system vibrates normally when given energy without outside
interference. - resonance:Timing force to be the same as natural frequency.
- sympathetic vibrations
Introduction
Many systems have a tendency to vibrate. When the forced vibration frequency is the same as the natural frequency,
the amplitude of vibration can increase tremendously. A well-known example of this situation is pushing a person
on a swing,Figure11.10. We know from study of simple pendulums that without being pushed, the person in the
swing rocks back and forth with a frequency that depends on gravity and the length of the chain.
f= 21 π√
g
LThis is one example of anatural frequency–the frequency at which a system vibrates normally when given energy
without outside interference.
Pushing on the person in the swing will affect the amplitude of the swinging. This is called forced vibration –when a
periodic force from one object (the person pushing) affects the vibration of another object (the person swinging). To
get the most effect, the person pushing will start just at the very back of the swing. In other words, the frequency
of how often they push is exactly the same as the frequency of the swing. Suppose they do not push at the right
time, but instead push at some other frequency. That would mean that sometimes they are pushing forward when
the swing is still going backward. In that case, the swing would slow down –i.e. the amplitude of the swing will be
reduced.
Timing the pushes to be the same as the natural frequency is calledresonance. For this reason, the natural frequency
is also known as the resonant frequency. If the pushes are timed just right, then even if each individual push is small,
the vibration will get larger with each push.