Examples of Forced Oscillations & Resonance
- Resonance occurs for any forced oscillation where the frequency of the driving force is equal to the natural frequency of the oscillator
- For example, a glass smashing from a high pitched sound wave at the right frequency
- Some other practical examples of forced oscillations and resonance include:
- An organ pipe
- Radio receivers
- Microwave oven
- Magnetic resonance imaging (MRI)
- In an organ pipe
- Air molecules vibrate in an air column setting up a stationary wave in the pipe
- This causes the air molecules to resonate leading to an increase in amplitude of sound
Standing waves forming inside an organ pipe from resonance
- Radio receivers
- The radio is “tuned” by setting its natural frequency equal to that of a radio station
- The radio tuned so that the electric circuit resonates at the same frequency as the specific broadcast
- 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 i.e. microwaves of a particular frequency that 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
Barton's Pendulums
- A mechanical system commonly used to show resonance is Barton's pendulums
- A set of light pendulums labelled A-E are suspended from a string
- A heavy pendulum X, with a length L, is attached to the string at one end and will act as the driving pendulum
- When pendulum X is released, it pushes the string and begins to drive the other pendulums
- Most of the pendulums swing with a low amplitude but pendulum C with the same length L has the largest amplitude
- This is because its natural frequency is equal to the frequency of pendulum X (the driving frequency)
Barton's pendulums helps display resonance
- The phase of the oscillations relative to the driver are:
- Pendulums E and D with lengths < L are in phase
- Pendulum C with length = L is 0.5π out of phase
- Pendulums B and A with lengths > L are π out of phase
