# 5.24 Resonance

## Resonance

• The frequency of forced oscillations is referred to as the driving frequency, f, or the frequency of the applied force
• All oscillating systems have a natural frequency, f0, this is defined as the frequency of an oscillation when the oscillating system is allowed to oscillate freely
• Oscillating systems can exhibit a property known as resonance • When the driving frequency approaches the natural frequency of an oscillator, the system gains more energy from the driving force
• Eventually, when they are equal, the oscillator vibrates with its maximum amplitude, this is resonance
• Resonance is defined as:

When the frequency of the applied force to an oscillating system is equal to its natural frequency, the amplitude of the resulting oscillations increases significantly

• For example, when a child is pushed on a swing:
• The swing plus the child has a fixed natural frequency
• A small push after each cycle increases the amplitude of the oscillations to swing the child higher. This frequency at which this push happens is the driving frequency
• When the driving frequency is exactly equal to the natural frequency of the swing oscillations, resonance occurs
• If the driving frequency does not quite match the natural frequency, the amplitude will increase but not to the same extent as when resonance is achieved
• This is because, at resonance, energy is transferred from the driver to the oscillating system most efficiently
• Therefore, at resonance, the system will be transferring the maximum kinetic energy possible

#### Resonance Effects

• Resonance occurs for any forced oscillation where the frequency of the driving force is equal to the natural frequency of the oscillator
• Examples include:
• An organ pipe, where air resonates down an air column setting up a stationary wave in the pipe
• Glass smashing from a high pitched sound wave at the right frequency
• A radio tuned so that the electric circuit resonates at the same frequency as the specific broadcast Standing waves forming inside an organ pipe from resonance ### Get unlimited access

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