Dulku – Physics 20 – Unit 4 – Topic J
Dulku – Physics 20 – Unit 4 – Topic J
Specific Outcome:
i. I can define mechanical resonance.
Mechanical Resonance
Nodes and Antinodes
Each transverse wave contains:
nodes = points of zero amplitude caused
by destructive interference (at the rest
position)
antinodes = points of maximum
amplitude caused by constructive
interference (at the top and bottom)
Dulku – Physics 20 – Unit 4 – Topic J
Nodes and Antinodes
Standing Waves
Forced Frequency
Dampening
Resonant Frequency
Pendulums
Quartz Crystals
Bridges and Towers
Mechanical Resonance
Nodes and Antinodes
Two transverse waves with antinodes that
are out of phase:
Destructive interference occurs:
Here, the two waves are staggered by ½λ, so
they seem to cancel out
Dulku – Physics 20 – Unit 4 – Topic J
1
Nodes and Antinodes
Two transverse waves with antinodes that
are in phase:
Constructive interference occurs:
Standing Waves
A wave formed by constructive interference
is called a standing wave
A standing wave pattern requires two
overlapping transverse waves to be:
approaching each other (i.e. opposite
directions)
in phase (i.e. on the same side of the
equilibrium position line)
Dulku – Physics 20 – Unit 4 – Topic J
Standing Waves
Dulku – Physics 20 – Unit 4 – Topic J
Standing Waves
Standing waves make it appear that a wave is
in the same location
In reality, two waves move towards one
another
The antinodes of the two waves simply add
together while they are overlapping
Dulku – Physics 20 – Unit 4 – Topic J
Dulku – Physics 20 – Unit 4 – Topic J
2
Standing Waves
ex. The distance between adjacent nodes on a standing
wave is 1.50 m. The frequency is 50.0 Hz.
a) Calculate the wavelength.
Standing Waves
ex. The distance between the second node and the
sixth node is 50 cm. Find the wavelength of the
wave.
λ = 2(1.50 m) = 3.00 m
b) Calculate the speed of the wave.
v = fλ = (50.0 Hz)(3.00 m) = 150 m/s
50 cm
50 cm = 2λ
λ=
50 cm
2
= 25 cm
Dulku – Physics 20 – Unit 4 – Topic J
Dulku – Physics 20 – Unit 4 – Topic J
Forced Frequency
Forced Frequency
A pendulum’s amplitude may be altered by
two different means:
forced frequency
dampening
Over time, a pendulum’s amplitude becomes
reduced because energy is lost
Frequency and period remain the same, since
they do not depend on energy
Dulku – Physics 20 – Unit 4 – Topic J
The frequency of a pendulum is based on
length and gravity
The amplitude may be corrected by having
another object apply an external non-zero
net force to the pendulum (physical contact)
The term for this is “forced frequency”
because the external force is applied at the
same frequency as the pendulum itself
Dulku – Physics 20 – Unit 4 – Topic J
3
Forced Frequency
Dampening
The external object must physically be
synchronized to the pendulum
The pendulum may also reduce its amplitude,
by doing work on its surroundings
The higher the external force, the higher the
amplitude of the pendulum
This means a loss of energy by the system
Dulku – Physics 20 – Unit 4 – Topic J
Resonant Frequency
All matter vibrates (oscillates)
Each object has a natural frequency at which
it vibrates, called the resonant frequency
The physical properties of each object
determine this resonant frequency
The amplitude is quite low, so we don’t
usually notice the oscillation
Dulku – Physics 20 – Unit 4 – Topic J
Since amplitude is being reduced, the
pendulum is being dampened
Dulku – Physics 20 – Unit 4 – Topic J
Resonant Frequency
If a forced frequency matches the natural
resonant frequency object well, it may
create a very large amplitudes
If this happens, we have reached mechanical
resonance
The effect may tear the object apart
Dulku – Physics 20 – Unit 4 – Topic J
4
Pendulums
All pendulums of the same length vibrate at
the same frequency, regardless of mass
Two pendulums with different lengths vibrate
at different resonant frequencies
Pendulums
If two pendulums are connected to the same
surface, one pendulum may increase the
amplitude of the other pendulum through
mechanical resonance:
Friction and temperature changes can affect
the amplitude of a pendulum
The resonant frequency of a pendulum
depends only on its length
Dulku – Physics 20 – Unit 4 – Topic J
Quartz Crystals
Quartz crystal is a mineral naturally found in
the Earth’s crust
Quartz crystals are piezoelectric; they
oscillate when a voltage is applied to them
A quartz crystal only needs a voltage to keep
the oscillation constant
At the correct voltage, the oscillation may
have a period of exactly 1 second
Dulku – Physics 20 – Unit 4 – Topic J
Dulku – Physics 20 – Unit 4 – Topic J
Quartz Crystals
Quartz crystals are used in clocks, because
they:
can be cut very small
have a very accurate oscillation
Artificial ceramic crystals may also exhibit a
piezoelectric effect
Materials science studies this property
Dulku – Physics 20 – Unit 4 – Topic J
5
Bridges and Towers
An office tower needs to be designed so that
the wind’s oscillation does not match the
natural resonant frequency of the building
Bridges are designed to allow wind to pass
through as much as possible
Newer buildings incorporate dampers (ex.
pools of water, giant swaying masses)
Dulku – Physics 20 – Unit 4 – Topic J
Bridges and Towers
A bridge may collapse if the wind’s
oscillation matches
ex. Tacoma Narrows bridge
Earthquakes may also affect towers and
bridges
ex. Taipei 101 tower in 2008
Dulku – Physics 20 – Unit 4 – Topic J
6