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## Waves and Sound

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### Waves and Sound Ch. 15-16 Types of Mechanical Waves A mechanical wave is a wave that requires a medium Transverse waves the displacement of the medium is ... – PowerPoint PPT presentation

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Title: Waves and Sound

1
Waves and Sound
• Ch. 15-16

2
Types of Mechanical Waves
• A mechanical wave is a wave that requires a
medium
• Transverse waves the displacement of the medium
is perpendicular to the direction the wave
travels
• Longitudinal waves the motion of the medium is
back and forth in the same direction as the wave
• Wave speed ? particle speed
• Waves are disturbances transport energy (but not
matter) from one region to another

3
Periodic Waves
• Periodic/Sinusoidal wave
• Wave has constant velocity, but every particle
undergoes simple harmonic motion
• Wavelength distance from point on one wave
shape to identical pt. on the next
• Frequency - number of cycles per unit time
• Velocity

4
Mathematical Description
wave function
• Wave equation
• Model for any wave (periodic or non-periodic,
electromagnetic, sound, on string, in water)

5
Speed of Transverse Waves and Wave Energy
• (speed of wave on string)
• F is tension and µ is mass per unit length
• Waves transport energy from one place to another
• (avg. power of wave on
string)
• Intensity the average rate at which energy is
transported by the wave, per unit of surface area
• (inverse-square law for intensity)

6
Reflection
Boundary conditions whether the end is fixed
(right) or free (left)
7
Interference and Superposition
• Interference two or more waves passing through
the same region
• Principle of Superposition when two waves
overlap, the displacement at any pt is the sum of
the individual waves displacements

8
Free Response
9
Standing Waves
• Pattern resulting from the combination of the
reflected wave and the original wave
• Nodes pts where amplitude never changes
• Antinodes pts where string fluctuates up to the
amplitude and then back down with each passing
wave body
• Does not appear to move, so is called a standing
wave (as opposed to a traveling wave last slide)

10
Standing Waves
• Operate based on the principle of superposition
(see right)
• Nodes occur at x0, ?/2, ?, 3?/2,
• Where do antinodes occur?

11
Normal Modes
• n1,2,3, (standing wave, fixed at
both ends)
• L is length of string, n is of antinodes
• n1,2,3,
• f1 is the fundamental frequency
• These frequencies are harmonics within the
harmonic series
• f2 is the 2nd harmonic and 1st overtone f3 is
the third harmonic and the second overtone

12
Free Response
• If a string forms a standing wave with 3
antinodes and a wavelength of 4 cm, how long is
the string?
• A standing wave travels at 5 m/s on a 1 m long
string. What is the frequency of the 2nd overtone?

13
Normal Modes
• (string fixed at both ends)
• Normal mode motion in which all particles in a
system move sinusoidally with the same frequency
• see previous diagram
• not the case for musical instruments
• What are timbre and harmonic content?

14
Sound what? Sound!
15
Sound Waves
• Sound is a longitudinal wave
• 20 20,000 Hz is the audible range
• Displacement amplitude the max. displacement of
a particle from its equilibrium position
• Useful to describe sound waves in terms of
pressure differences
• Pressure amplitude max pressure fluctuation

16
Speed of Sound
• In a fluid
• In a solid rod
• In an ideal gas
• At 20C, speed of sound in air is 344 m/s
• Does sound travel fastest in a gas, a liquid, or
a solid? Slowest?

17
Sound Intensity
• A low-frequency sound need a large amplitude to
have the same intensity as a high-frequency sound
(b/c )
• Decibel scale
• logarithmic scale
• 10 dB x 10 intensity 20 dB x 100 intens.

18
Free Response
• A concert is recorded as having a decibel level
of 170 dB. Since I0 is 10-12 W/m², what is the
intensity of the sound?
• If one person speaks at 8x10-4 W/m² and a second
person yells at 4x10-3 W/m², how many decibels
louder is the second?

19
Standing Sound Waves
• In same way that transverse standing waves form,
longitudinal standing waves can form
• Pressure nodes vs. Displacement nodes
• Pressure node is a point in a standing sound wave
at which pressure and density do not vary
• Pressure antinode is a point at which pressure
and density vary the greatest

20
Open Resonators
• Open pipe open at both ends
• Displacement nodes are at each end
• Ex organ, flute, recorder, ocarina?

21
Stopped Resonators
• Stopped pipe one open end, one closed
• Antinode at the open end and node at closed end
• Ex Oboe, clarinet

22
Resonance
• Similar to concept of driven oscillation
• If the frequency of a speaker, voice, etc.
matches one of the normal-mode frequencies of
resonator (i.e. pipe), then the resonator
vibrates with maximum amplitude.
• Aretha Franklin example

23
Interference
• Constructive interference two or more waves
meet so that the resulting wave is larger than
either of the originals (i.e. crest to crest,
trough to trough)
• Waves are in phase
• Destructive Interference two or more waves seem
to cancel each other out (i.e. crest meets
trough)
• Waves are out of phase

24
Interference
• Constructive/ in phase waves differ by an
integer multiple of ? (?, 2?, 3?, )
• Destructive/ out of phase waves differ by an
integer multiple of ?/2 (?/2, 3?/2, 5?/2,)

25
Free Response
• Two loudspeakers are positioned as below. The
both produce a frequency of 784 Hz. The speed of
sound in air is 344 m/s. a) At what distances
from B will there be destructive interference? b)
What distances will produce constructive
interference? c) If the frequency is made low
enough, there will be no positions along the line
BC at which destructive interference occurs. How
low must this frequency be?

26
Beats
• When two sounds destructively interfere slightly
out of phase, the resulting superposition (wave)
has a different frequency, the beat frequency

27
Doppler Effect
• Simply when a source of sound and a listener
are in relative motion, the perceived frequency
differs from the actual
• Think of a boat moving towards and away from
shore
• Applies to light as well red shifting

28
Free Response
• A car alarm is emitting sound waves of frequency
520 Hz. You are on a motorcycle, traveling
directly away from the car. How fast must you be
traveling if you detect a frequency of 490 Hz?