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The condition when the frequency of an external force matches the natural frequency?
Wiki User
∙ 13y ago
This phenomena is called resonance. In electrical theory it happens when a inductive reactance is equal to the capacitive reactance regardless whether the reactance's are in parallel or series. A very simple mathematical derivative can prove the general equation.
If XL is the inductive reactance and XC is the capacitive reactance then at resonance condition the following is true
Since
XL=2.π.f.L
XC=1/(2.π.f.C)
At resonance
XL=XC
Thus
2.pi.f.L=1/( 2.π.f.C)
f2=1/( 4.π2.L.C)
fo=1/( 2.π.√(L.C))
One must take care that for series circuits, impedance at resonance will be equal to the internal resistance while with parallel circuits it is equal to the dynamic resistance RD. Note that we call it resistance since the inductive and capacitive reactance's are equal thus causing a zero phase angle similar to a resistance. In series circuits the impedance becomes minimum, while in parallel the impedance becomes maximum.
Resonance can also be considered as a voltage magnification in series circuits and great caution must be taken since the voltage across impedances can massively increase
A circuit have a 1Ω internal resistance and 10mH inductor, a 10uF capacitor, based on the above formula it will resonate at 503.3Hz. So lets apply 503.3Hz at 100V to the circuit and see what happens across the inductor.
XL = 2. π.f.L=2. π. 503.3Hz.10mH=31.61Ω
XC=1/(2.π.f.C)=1/(2. π. 503.3Hz.10uF) = 31.61Ω
Let j= √ (-1) for the complex notation
The impedance of inductor is
= r + jXL =1 +j31.61 = 31,633∟88.188° Ω
The impedance of the capacitor = -jXC=- j31.61 =31.61 ∟-90°Ω
The total impedance is 1 + j31.61 - j31.61 = 1 +j0 = 1 ∟0°
The current = 100∟0° / 1 ∟0°=100∟0°A
The voltage across the inductor
VL= I x Z = (100∟0°).(31,633∟88.188° Ω)=3163∟88.188° V
As you can see, even though 100V supply might not cause a deadly shock, 3163V across the inductor will be fatal.
Beware that harmonics exists in practical circuits, these are additional frequencies that is added to the fundamental to create a complex wave, often they are odd like 3rd and 5th harmonics. Beware of the term overtone, it is one out for example 2nd harmonic is the 1st overtone, This means 50Hz can have harmonics of 150Hz and 250Hz which can also go into resonance, so even if 50Hz is well outside resonance and will not create much voltage magnification across the inductor, one of the harmonics may be 250Hz and only 10V in magnitude which is about 10% of the 100V fundamental. Then a circuit with a 40mH inductor, 1 Ω resistance, 10uF capacitor can produce a 600V across the inductor because of that tiny harmonic.
In parallel circuits one should be careful for tanking, it is a process where electric field of the capacitor discharge to the inductor creating a magnetic field that will collapse to create a electric field again in the capacitor once again exchanging energy back and fourth. Resistance and loads normally damp the effect quickly but large reactance's and low resistance and very high load impedances can cause a train of ongoing sinus waves long after the power has been removed. This method have been applied in the construction of oscillator circuits
Often one can refer to other mechanical actions to explain what happens during resonance. If a parent pushes a kid on a swing, every cycle the kid swings the parent give a little push in the exact critical stage in the cycle to add extra energy in the direction the swing. Adding a little after every cycle can accumulate energy to let the kid swing very high.
If a wind turbulences creates a fixed frequency and blow onto a bridge, and as the wind push and pull. The bridge will be pushed into a direction, the wind will stop or pull and the bridge swing back but as the bridge turns at it's turning point to swing into the other direction again, the wind surge again and add energy to the motion, once the bridge get to its turning point again the wind stops and the bridge swings back and every cycle the wind surges up at exactly the right time to add energy to the swinging motion until the bridge is so heavily charged with kinetic energy that it destroy it self and collapse. In some areas, valleys, between buildings, constant wind speeds that give rise to turbulences due to fixed structures may result in stable frequencies of push and pull actions by the wind. If the frequency matches the natural frequency of a structure it will accumulate energy after each cycle. It can create massive damage or destruction.
This is also the reason soldiers may not march across a bridge just incase all that feet stepping at the same time will fall into resonance with some of the fundamental structures of the bridge.
More can be read about Tacoma Narrows Bridge that collapsed in 1940, because of a resonance effect caused by wind.
Wiki User
∙ 13y ago
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Resonant
When the frequency of light matches the natural frequency of molecules in a material light is?
Light is absorbed by the molecule.
When a forced vibrations matches an object's natural frequency does it resonate?
Yes!
What occurs when vibrations through an object match the object's natural frequency?
Any object in absence of external force vibrates with it's natural frequency. When the frequency of the external forced vibration matches the object's natural frequency, we say that resonance has occurred. In this situation the amplitude of the object's oscillation becomes larger. How much larger depends on the amplitude of the forced vibration.
When the frenquency of light matches the natural frequency of molecules in a material light is?
absorbed
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Absolutely not! Glass, for example (every wine glass has a different natural frequency), can be broken by a frequency that matches its own but nearby objects aren't affected by the same frequency.
How can we break glass using sound?
when the natural frequency of glass matches with the frequency of sound than glass can be shettered as it is due to the phenomenon of resonance
What physics principle is used when pumping your legs in rhythm with the natural frequency of a swing?
Resonance - when pumping a swing in rhythm with its natural frequency, it produces larger amplitudes.(def. - occurs when the frequency of a vibration forced on an object matches the object's natural frequency and a dramatic increase in amplitude occurs)
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A condition known as resonance, in which the object vibrates much stronger than at other frequencies.
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