CIE A Level Physics (9702) 2019-2021

Revision Notes

19.2.2 Resonance

Force Oscillations & Resonance

Some practical examples of forced oscillations and resonance include:

  • Radio receivers
    • The radio is “tuned” by setting its natural frequency equal to that of a radio station
    • The resonance of the radio waves allows the signal to be amplified by the receiver to listen
  • Microwave oven
    • Conventional cooking methods involve transferring heat energy by conduction or convection
    • A microwave transfers heat energy by radiation ie. microwaves of a particular frequency which resonate with the water molecules in food
  • Magnetic resonance imaging (MRI)
    • This type of scanner is a widely used medical diagnostic tool used to look at organs and structures inside the body
    • The atomic nuclei in the body are made to resonate with incoming radio waves (of the order of 100 MHz)
    • The signals are then sent to a computer to create digital scans and provide a detailed image of the scanned area

Resonance

  • In order to sustain oscillations in a simple harmonic system, a periodic force must be applied to replace the energy lost in damping
    • This periodic force does work on the resistive force decreasing the oscillations
  • These are known as forced oscillations, and are defined as:

Periodic forces which are applied in order to sustain oscillations

  • For example, when a child is on a swing, they will be pushed at one end after each cycle in order to keep swinging and prevent air resistance from damping the oscillations
    • These extra pushes are the forced oscillations, without them, the child will eventually come to a stop
  • The frequency of forced oscillations is referred to as the driving frequency (f)
  • 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 resonance is achieved, a maximum amplitude of oscillations can be observed
  • Resonance is defined as:

When the driving frequency applied 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
    • If the driving frequency does not quite match the natural frequency, the amplitude will increase but not to the same extent at 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
  • A graph of driving frequency f against amplitude a of oscillations is called a resonance curve. It has the following key features:
    • When f < f0, the amplitude of oscillations increases
    • At the peak where f = f0, the amplitude is at its maximum. This is resonance
    • When f > f0, the amplitude of oscillations starts to decrease
  • Damping reduces the amplitude of resonance vibrations
  • The height and shape of the resonance curve will therefore change slightly depending on the degree of damping
    • Note: the natural frequency f0 will remain the same
  • As the degree of damping is increased, the resonance graph is altered in the following ways:
    • The amplitude of resonance vibrations decrease, meaning the peak of the curve lowers
    • The resonance peak broadens
    • The resonance peak moves slightly to the left of the natural frequency when heavily damped

Pros & Cons of Resonance

  • Forced oscillations and resonance can be very useful when large-amplitude oscillations are intended
  • However, large-amplitude oscillations can be very dangerous in structures, such as bridges, where resonance should be avoided

Advantages

  • Resonance is useful for:
    • Producing ultrasound in a piezoelectric crystal
    • Increasing the intensity of sound in musical instruments
    • Pushing a child on a swing to make them go higher
  • Resonance is a major component of machines and appliances such as:
    • Radio receivers
    • Microwave ovens
    • Magnetic resonance imaging (MRI) scanners

Disadvantages

  • Resonance is a major concern in constructing structures, such as bridges and roofs
  • An example of this is the Millennium Bridge in London which opened in June 2000:
    • When pedestrians walked along the bridge, it began to sway from side to side
    • The pedestrians therefore also swayed with the bridge in step, causing the amplitude of the bridge’s oscillation to gradually increase
    • After closing for a few years, engineers eventually put ‘dampers’ on the bridge to absorb the energy of these oscillations
    • Now the bridge is rigid and safe to walk on

Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
Close

Join Save My Exams

Download all our Revision Notes as PDFs

Try a Free Sample of our revision notes as a printable PDF.

Join Now
Go to Top