Sound Interference Positions of zero displacement resulting from destructive interference are referred to as: A. antinodes B. nodes C. supercrests D. supertroughs

Sound Interference Positions of zero displacement resulting from destructive interference are referred to as: A. antinodes B. nodes C. supercrests D. supertroughs

Forced Vibration and Resonance 3U Physics

Natural Frequencies Nearly all objects, when disturbed, will vibrate. Objects tend to vibrate at a particular frequency (or set of frequencies) that depends on the properties of the object.

Natural Frequencies Nearly all objects, when disturbed, will vibrate. Objects tend to vibrate at a particular frequency (or set of frequencies) that depends on the properties of the object: the material (which affects the speed of the wave) the material (which affects the speed of the wave) the length (which affects the wavelength) the length (which affects the wavelength) This frequency is known as the natural or resonant frequency of the object.

Resonance: Example For example, the sound wave produced by a vibrating tuning fork will cause an identical tuning fork to start vibrating.

Resonance An object that is forced at its natural frequency will resonate (vibrate) at that frequency (with increasing ? if the forcing continues).

Resonance An object that is forced at its natural frequency will resonate (vibrate) at that frequency (with increasing amplitude if the forcing continues).

Resonance Consider the forced vibration of a child on a swing – pushing at the natural frequency increases the amplitude. We use a similar technique to “rock” a car that is stuck in the snow. And when a large truck passes your house, you may have noticed that the windows rattle.

Resonance An object that is forced at its natural frequency will resonate (vibrate) at that frequency (with increasing amplitude if the forcing continues). Mechanical resonance must be taken into account when designing bridges,airplane propellers, helicopter rotor blades, turbines for jet engines,plumbing systems, and many other types of equipment. A dangerous Mechanical resonance must be taken into account when designing bridges,airplane propellers, helicopter rotor blades, turbines for jet engines,plumbing systems, and many other types of equipment. A dangerous resonant condition may result if this is not done. resonant condition may result if this is not done. e.g. The Tacoma-Narrows Bridge:

Countering Resonance To help decrease the amplitude of vibrations due to resonance, some buildings have a mass damper, usually consisting of large shock absorbers or a pendulum made out of concrete or steel. These dampers develop sympathetic vibrations, which take energy from the building when it vibrates, thus decreasing its amplitude. The dampers are designed to take the energy before it can return to the building. To help decrease the amplitude of vibrations due to resonance, some buildings have a mass damper, usually consisting of large shock absorbers or a pendulum made out of concrete or steel. These dampers develop sympathetic vibrations, which take energy from the building when it vibrates, thus decreasing its amplitude. The dampers are designed to take the energy before it can return to the building

Standing Waves The natural or resonant frequencies of an object are those that produce standing waves (when the wave interferes with its own reflection in the medium).

Nodes and Antinodes The points of zero displacement are nodes. The points of maximum displacement are antinodes.

Nodes and Antinodes The points of zero displacement are nodes. The points of maximum displacement are antinodes. Because it is difficult to draw a standing wave in motion, they are often illustrated showing both extremes at once:

Wavelengths How many wavelengths are illustrated in the diagram below?

Wavelengths 2

Standing Waves These natural frequencies are called harmonics. The 1 st harmonic is called the fundamental frequency:

String Harmonics The first three harmonics for a vibrating string (which is secured at each end and therefore has to have a node at each end) are: = =

String Harmonics The first three harmonics for a vibrating string (which is secured at each end and therefore has to have a node at each end) are: = 2L = 2L = =

String Harmonics The first three harmonics for a vibrating string (which is secured at each end and therefore has to have a node at each end) are: = 2L = 2L = L = L = 2L/3 = 2L/3

String Harmonics Recall that the first three harmonics for a vibrating string (which is secured at each end and therefore has to have a node at each end) are: = 2L so f = v/2L = 2L so f = v/2L = L so f = v/L = L so f = v/L = 2L/3 so f = 3v/2L = 2L/3 so f = 3v/2L

Practice Question 1 A string resonates with a fundamental frequency of 512 Hz. The speed of sound in the string is 1750 m/s. What is the length of the string?

Practice Question 1 A string resonates with a fundamental frequency of 512 Hz. The speed of sound in the string is 1750 m/s. What is the length of the string?

Practice Question 1 A string resonates with a fundamental frequency of 512 Hz. The speed of sound in the string is 1750 m/s. What is the length of the string?

Practice Question 2 A guitar string has a frequency of 256 Hz and a length of 49.1 cm. A guitarist reduces the string's length by 12.8 cm by pressing on the string. What is the new frequency?

Practice Question 2 A guitar string has a frequency of 256 Hz and a length of 49.1 cm. A guitarist reduces the string's length by 12.8 cm by pressing on the string. What is the new frequency? For the 1 st length,

Practice Question 2 A guitar string has a frequency of 256 Hz and a length of 49.1 cm. A guitarist reduces the string's length by 12.8 cm by pressing on the string. What is the new frequency? For the 2 nd length,

Practice Question 2 Note that reducing the length increased the fundamental frequency.

More Practice Homework: Resonance Isn’t it hypnotic?