Resonance (Edexcel International A Level Physics)

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