Sound Interference

1
Sound Interference

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

2
Sound Interference

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

3
Forced Vibration and Resonance

• 3U Physics

4
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.

5
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 length (which affects the wavelength)
• This frequency is known as the natural or
  resonant frequency of the object.

6
Resonance Example

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

7
Resonance

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

8
Resonance

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

9
Resonance

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

10
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
• resonant condition may result if this is not
  done.
• e.g. The Tacoma-Narrows Bridge

11
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.
• http//www.youtube.com/watch?vO9FrMkhQoA4
• http//www.youtube.com/watch?vnHSGd2X1nc8feature
  related
• http//www.youtube.com/watch?voXV45t6wlWUfeature
  related

12
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).

13
Nodes and Antinodes

• The points of zero displacement are nodes.
• The points of maximum displacement are antinodes.

14
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

15
Wavelengths

• How many wavelengths are illustrated in the
  diagram below?

16
Wavelengths

• How many wavelengths are illustrated in the
  diagram below?
• 2

17
Standing Waves

• These natural frequencies are called harmonics.
• The 1st harmonic is called the fundamental
  frequency

18
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
• l
• l
• l

19
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
• l 2L
• l
• l

20
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
• l 2L
• l L
• l 2L/3

21
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
• l 2L so f v/2L
• l L so f v/L
• l 2L/3 so f 3v/2L

22
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?

23
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?

24
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?

25
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?

26
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 1st length,

27
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 2nd length,

28
Practice Question 2

• Note that reducing the length increased the
  fundamental frequency.

29
More Practice

• Homework Resonance

Isnt it hypnotic?