Applications of Waves and
Vibrations
Notes
Waves

Characteristics
• Wavelength (λ)
• Frequency (f)
• Period (T)
• Wave speed (v)
• Phase (Φ)
Interference ?


When 2 or more waves in a medium
pass through the same point at the
same time they overlap >> interference
Interference can be either:
• Constructive
• Destructive
Interference - Constructive

When the wave concurrence results in an additive effect
such that the amplitude of the resulting wave is greater
than the originals
Interference - Destructive

When the wave concurrence results in an additive effect
such that the amplitude of the resulting wave is less than
the originals
How are the overlap effects
shown?

Add the corresponding amplitudes for
each wave at the point of interest
• Law of Superposition of waves
Wave1
Wave2
=
Result
How is wave interference
useful?

In optics
• When determining if machined parts are flat –
examine the optical response when light is shone
on the metal (Fig 9-21)

In acoustics
• when designing auditoriums to eliminate sound
•
•
dead spots where sound is out of phase and
muffled
When reducing “noise” in aircraft with sound
generators
Tuning musical instruments by using “beats”
between string frequencies
Forced Vibrations


If an outside force is applied at regular
intervals to an object, the object will be
forced to vibrate at the frequency of the
outside force
Can be good or bad!
Forced Vibrations - good
examples

Musical instruments – piano or guitar
• Struck string causes the sound board to vibrate at
the string frequency, increasing volume

Reed instruments – saxophone, guitar
• Reed vibrations cause columns of air to vibrate
inside the instrument, amplifying the sound.

Loudspeakers
• Electric signals force speaker cones to vibrate,
thus setting up air motion - (longitudinal waves)
which are heard as sound.
Forced Vibrations – bad
examples

Mechanical systems
• Forced vibrations cause the machines to
vibrate at unwanted frequencies
• Can cause overheating, undue wear, misalignment
• Rubber mounts are used to isolate the
mechanical parts or damp out the vibrations
? Natural Frequency of an object

Frequency at which an object continues
to vibrate on its own after being set in
motion, for example:
• Swing
• Pendulum
• Bad shock absorbers
Combine natural frequency and
forced vibration

If both frequencies match, resonance
occurs, and the amplitude of vibration
increases dramatically
• Tacoma Narrows bridge disaster

If the frequencies do not match, little energy
is transferred from the forced vibration to
the object
• Try to “pump” a swing at some frequency that is
not natural to the swing – little effect!
Resonance

Mechanical techniques are used to
minimize this phenomenon in engines
• Harmonic balancers, precision flywheels,
cylinder firing order

Resonance is used extensively in
electronic circuits for tuning, phase
matching, etc
Summary Terms

Interference

Forced vibrations
Resonance

• Constructive
• Destructive
• Superposition