Sound InterferenceSound Interference

Positions of zero displacement Positions of zero displacement resulting from destructive resulting from destructive interference are referred to as:interference are referred to as:

A. antinodes A. antinodes B. nodesB. nodes

C. supercrests C. supercrests D. D. supertroughssupertroughs

Sound InterferenceSound Interference

Positions of zero displacement Positions of zero displacement resulting from destructive resulting from destructive interference are referred to as:interference are referred to as:

A. antinodes A. antinodes B. nodesB. nodes

C. supercrests C. supercrests D. D. supertroughssupertroughs

Forced Vibration Forced Vibration and Resonanceand Resonance

3U Physics3U Physics

Natural FrequenciesNatural Frequencies

Nearly all objects, when disturbed, will Nearly all objects, when disturbed, will vibrate.vibrate.

Objects tend to vibrate at a particular Objects tend to vibrate at a particular frequency (or set of frequencies) that frequency (or set of frequencies) that depends on the properties of the object. depends on the properties of the object.

Natural FrequenciesNatural Frequencies

Nearly all objects, when disturbed, will Nearly all objects, when disturbed, will vibrate.vibrate.

Objects tend to vibrate at a particular Objects tend to vibrate at a particular frequency (or set of frequencies) that frequency (or set of frequencies) that depends on the properties of the object:depends on the properties of the object:

the material (which affects the speed of the the material (which affects the speed of the wave)wave)

the length (which affects the wavelength)the length (which affects the wavelength)

This frequency is known as the This frequency is known as the natural natural or or resonant frequencyresonant frequency of the object. of the object.

Resonance: ExampleResonance: Example

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

ResonanceResonance

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

ResonanceResonance

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

ResonanceResonance

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

Consider the forced vibration of a Consider the forced vibration of a child on a swing – pushing at the child on a swing – pushing at the natural frequency increases the natural frequency increases the amplitude.amplitude.

ResonanceResonance

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

Or the Tacoma-Narrows Bridge:Or the Tacoma-Narrows Bridge:

ResonanceResonance

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

Or: Or: http://www.youtube.com/watch?v=O9FrMkhQoA4

http://www.youtube.com/watch?v=nHSGd2X1nc8&feature=relatedhttp://www.youtube.com/watch?v=oXV45t6wlWU&feature=related

Standing WavesStanding Waves

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

Nodes and AntinodesNodes and Antinodes

The points of zero The points of zero displacement are displacement are nodesnodes..

The points of maximum The points of maximum displacement are displacement are antinodesantinodes..

Nodes and AntinodesNodes and Antinodes

The points of zero The points of zero displacement are displacement are nodesnodes..

The points of maximum The points of maximum displacement are displacement are antinodesantinodes..

Because it is difficult to Because it is difficult to draw a standing wave in draw a standing wave in motion, they are often motion, they are often illustrated showing both illustrated showing both extremes at once:extremes at once:

WavelengthsWavelengths

How many wavelengths are illustrated How many wavelengths are illustrated in the diagram below?in the diagram below?

WavelengthsWavelengths

How many wavelengths are illustrated How many wavelengths are illustrated in the diagram below?in the diagram below?

22

Standing WavesStanding Waves

These natural frequencies are called These natural frequencies are called harmonicsharmonics..

The 1The 1stst harmonic is called the harmonic is called the fundamental frequency:fundamental frequency:

String HarmonicsString Harmonics

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

==

==

==

String HarmonicsString Harmonics

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

= 2= 2LL

==

==

String HarmonicsString Harmonics

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

= 2= 2LL

= = LL

= 2= 2LL/3/3

String HarmonicsString Harmonics

Recall that the first three harmonics for a Recall that the first three harmonics for a vibrating string (which is secured at each vibrating string (which is secured at each end and therefore has to have a node at end and therefore has to have a node at each end) are:each end) are:

= 2= 2L L soso f = v/ f = v/22LL

= = L L soso f = v/L f = v/L

= 2= 2LL/3 so f = 3/3 so f = 3vv/2/2LL

Practice Question 1Practice Question 1

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

Practice Question 1Practice Question 1

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

mHzf

vfv s

m

418.3512

1750

Practice Question 1Practice Question 1

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

mHzf

vfv s

m

418.3512

1750

mmL 71.1)418.3(21

21

Practice Question 2Practice Question 2

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

Practice Question 2Practice Question 2

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

For the 1For the 1stst length, length, smHzmfLfv 4.251)256)(491.0(22

Practice Question 2Practice Question 2

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

For the 2For the 2ndnd length, length,Hz

mmL

vvffv s

m

346)128.0491.0(2

4.251

2

Practice Question 2Practice Question 2

Note that reducing the length Note that reducing the length increasedincreased the fundamental the fundamental frequency.frequency.

HzmmL

vvffv s

m

346)128.0491.0(2

4.251

2

More PracticeMore Practice

Homework: ResonanceHomework: Resonance

Isn’t it hypnotic?