RESONANCE & SOUND
Amplification
AIR COLUMN
 When a wave source is held at the open end of a pipe, it
sends down a wave that reflects from the closed end of the
pipe.
 If the length of the pipe is just right, the reflected wave can
combine with the incident wave to establish a standing
wave pattern.
 The sound you hear depends on the length of the air
column in the pipe relative to the length of the standing
wave.
AIR COLUMN
 If an antinode occurs at the open end of the pipe a point of
resonance (resulting from constructive interference) occurs
at the open end of the pipe and the sound appears to be
amplified.
 However, if the open end of the pipe does not coincide with
the position of an antinode, then little sound can be heard
because the incident wave
AIR COLUMN
NODES & ANTINODES
 Nodes are located every half-wavelength from the end at
which the wave is reflected
 Antinodes in the air column are located one quarter-
wavelength from the end of the pipe where reflection
occurs, and then every half-wavelength from that point
AIR COLUMN
A tuning fork with a frequency of 384 Hz is held
above an air column. As the column is lengthened,
a closed-pipe resonant point is found when the
length of the air column is 67.5 cm.
What are possible wavelengths for this data? If the
speed of sound is known to be slightly greater than
300 m/s, what is the actual wavelength, and the
actual speed of sound?
AIR COLUMN
A tuning fork with a frequency of 256 Hz is held over
a closed air column. The temperature of the air is
19C. Find the shortest length of the column that
will produce resonance.
STRING INSTRUMENTS
 A string of a musical instrument is simply a tightly
stretched spring for which the simplest standing
wave possible is a single antinode with a node at
either end.
 The fundamental frequency is the lowest
frequency produced by a particular instrument.
STRING INSTRUMENTS
 The frequencies above the fundamental
frequency that may exist simultaneously with the
fundamental frequency are called overtones.
STRING INSTRUMENTS
1. A string of length 0.860 m is stretched tightly
between two fixed ends. The string is plucked
and a vibration is created that travels with a
speed of 125 m/s along the string.
a) Sketch the fundamental wave and first two
overtones produced in the string.
b) Use your sketches to determine the fundamental
frequency and frequencies of the overtones.
c) Are the overtones harmonics of the fundamental
frequency?
WIND INSTRUMENT
 Wind instruments produce different musical notes by
changing the lengths of air columns
 The distance from one antinode to the next is one-half a
wavelength. Thus, the longest wavelength that can
resonate in an open pipe is twice as long as the pipe.
WIND INSTRUMENT
WIND INSTRUMENT
 In a clarinet or oboe, for example, the effective length of
the pipe is changed by covering or uncovering holes at
various lengths down the side of the pipe.
 The strongest or most resonant frequency will be the wave
whose length is twice the distance from the mouthpiece to
the first open hole.
WIND INSTRUMENT
Use 344 m/s as the speed of sound in this case.
a) Sketch the fundamental wave and the first two
overtones for a vibrating closed-end air column
produced in a tube that is 0.860 m long.
b) Find the wavelengths and frequencies for these
resonances.
c) Are the overtones harmonics?
WIND INSTRUMENT
 Determine the length of an open-end air
column required to produce a fundamental
frequency (1st harmonic) of 480 Hz.
SPEED OF SOUND
SPEED OF SOUND
If an object is 6.56 m from the camera and sound
travels at 344 m/s, determine the length of time it
takes the emitted sound pulse to return to the
camera.
SPEED OF SOUND
SPEED OF SOUND
 What is the wavelength of a sound of frequency
225 Hz that is produced in air at a temperature of
20.0°C?
INTENSITY
Our ears are marvellous organs.
They can respond to the faintest of
whispers or the roar of a jet engine.
The ability to distinguish variations in
loudness is an important environmental
cue that humans and other animals use to
navigate in their surroundings.
INTENSITY
The intensity of a sound is the energy per
unit area that passes a point each second.
It has units of (J/m2)/s or J/s·m2,
which is the same as W/m2.
 Our ears can respond to sounds as faint as
one-trillionth of a watt per square metre
DECIBEL SCALE
DECIBEL SCALE
 The Greek letter beta,  , is commonly used to
represent sound intensity expressed in dB.
 The faintest sound that humans can hear
represents the start of the decibel scale and is
given a value of 0 dB.
 The decibel scale is a logarithmic scale that
corresponds to how our ears perceive loudness.
DECIBEL SCALE
DECIBEL SCALE
 In general, the smallest difference in loudness that
can be detected by the human ear is 1 dB.
 When using the decibel scale, every 3-dB increase
in SIL is a doubling in intensity.
 A 10-dB increase increases the intensity by 10
times.
DECIBEL SCALE
INTENSITY  LOUDNESS
 The terms “loudness” and “intensity” do not have the same
meaning.
 Loudness is a measure of the ear’s response to sound. Two
sounds can have equal intensity,
 but you may hear one sound as louder than another
because your ears can detect it better.
STANDING WAVES
node
antinode
STANDING WAVES
RESONANCE
RESONANCE
RESONANCE
RESONANCE