Why do things resonate at certain frequencies but not others?

Question

Im curious to how and why objects such as glass resonate at a certain frequency and is oblivious to any other. Also in relation, how does a radio receiver pick up certain frequencies by resonating at the same frequency? Thanks

Answer 1

Think of pushing a small tree. Theres a certain rythum you can push it to get the maximum amount of swing. The frequency of your pushing, how many times you push the tree per minute say, to get the maximum amount of swing is set by how heavy the tree is and how strong the tree trunk is. This is the resonant frequency of the swinging tree trunk.
If I put a weight on top of the tree the number of pushes/minute(frequency) to get the most swing would go down. If I made the tree trunk stronger the frequency would go up. It's kind of like this with most other things that resonate. You can model any resonator with a mass(the weight of the tree in this example), and a spring(the bending tree trunk in this example) and some kind of dampening(the bending tree trunk will generate heat and take power from the system). Dampening means that the resonator doesn't go forever if there is no pushing going on. Some resonators have little or no dampening but many do.
You can't push the tree at twice the number of pushes/minute and get the same effect. Just doesn't work.
In the case of a radio, the resonator in the receiver likes to wiggle at a certain frequency, like all resonators. In a radio signal, the signal is carried on one specific frequency. Other stations(signals) are carried at other frequencies. Although this isn't entirely accurate, think of all the radio signals in the air coming from the antenna to the receiver. The resonator wiggles at the tuned frequency and not the others. Electrically, this "shorts out" the unwanted frequencies(radio signals) and passes the desired frequency.

Answer 2

This is because every object is partly elastic, and thus it can oscillate if hit, just as a bell, or a string from a musical instrument. When it does so, there are deformation waves that propagate through it, with a speed determined by the material the object is made of. We can understand that the frequency at which the object will oscillate when hit corresponds to the inverse of the time taken by the waves to go from one side to the other, two ways.
So for each object, there is a particular frequency at which it will oscillate on its own when hit. It is actually its 'resonance frequency'. Same for the receiving circuit of a radio, that usually contains a piezo-electric resonator, a cristal (that resonates mechanically) and which mechanical deformations are coupled to the voltage applied to it.
Now, when you make an object resonate, you apply a sound wave to it, which frequency is exactly the resonance frequency. The mechanical deformations created by the periodic "pushes" from the wave propagate through the object, and come back exactly when there is another push. They build up, and build up, and sometimes, when the material is fragile, they can actually break it.
In a radio receiver, you can tune the resonance frequency of the piezo-electric circuit, usually by changing the value of a resistor. When a radio wave of a particular frequency reaches the antenna, a very small sinusoidal current will go through the circuit. And if its frequency is the resonance frequency of the circuit, it will build up until it becomes strong enough to be transformed into sound by the radio receiver.

Don't forget to take a look at the Wiki page for Resonance.

Answer 3

It's all about differential equations and boundary conditions.

Most resonators have some sort of a wave equation which governs how a sound wave or a light wave or a wave on a string or a quantum mechanical wave function behave within them. For simple examples, the solutions are often sines or cosines. For more complex examples, you can get Bessel functions and legendre and hermite polynomials and all sorts of things.

The quantization of the waves comes from the boundary conditions. For example.

In an organ pipe with closed ends or a wave on a string with both ends fixed or the infinite potential well in quantum mechanics, the boundary condition is that the wave function at either end is zero. This forces the wave to only have discrete allowed wavelengths. The wavelength must be an 2L/n, L is the length of the resonator and n is some integer. n=1 is the fundamental mode of the resonator and larger n are called harmonics. Play around with a jumprope and you'll see how this works.

In a glass or a hydrogen atom or something like that, there is the boundary condition that the angular wave functions must be single valued. f(theta) = f(theta + 2 pi). This also forces the wave into discrete modes.

Answer 4

..er start with the eqation for a harmonic wave?..y=acos(kx-w*t) ..(w=2pi*f) and(k=2*pi/lambda)
If u diff y 2wce wrt x and then t
you get y''=c^2gradsquared(x) (d2x by dy squared) where y''= 2nd diff wrt to time and c=wave speed. You can use this to work out the characteristic
speed of waves in different materials depending on stiffness, tension, density etc
In 3D it becomes y''=c^2(gradsquared phi) where phi is the amplitude. In a srtring or a glass or a metal plate the boundaries limit the profile of the wave set up.eg one complete half wave or one whole wave where the boundaries of the medium constrain the vibration or one quarter wave or 3/4 wave where one end is closed and the other free etc. This is called a standing wave. This defines the frequency f=c/lambda at which the system vibrates. If more energy than is lost due to damping is supplied to the system at this frequency it will resonate ie its amplitude will increase. Bluddy hell!.. OK for tuned circuits the resonant frequency occurs when the impedance (depends on f) is the same for both capacitor and coil. So 1/(2*pi*f*C)=2*pi*f*L
>f=1/2*pi*(sqrt(LC) where C= capacitance, L=inductance of coil.

Answer 5

All objects vibrate in tune with the frequency of the exciting force. This is called FORCED VIBRATION.

All objects have a frequency called natural frequency. If objects are excited with some force and then if the force is removed, the objects vibrate with a frequency natural to it.

If the natural frequency coincides with the exciting frequency, it is called RESONANCE.


The oscillation of electric current in an antenna is similar to the vibration of a rod or string.

A conduction current antinode exists at the center of the line and conduction current nodes exist at the ends when electro magnetic waves are excited on the line.

At any instant of time, charges of opposite sign are located on the two halves of the line.

Thus an antenna of length L can receive radio wave of wavelength λ, satisfying the condition L = λ/2.

In the field of radio, a number of methods exist for varying the natural frequencies of antenna. Basically, they consist in the connection of a self inductance coil or a condenser to the antenna.
By varying the inductance or capacitance, the natural frequency of the antenna may be varied within broad limits.

When the natural frequency of the antenna coincides with the exciting frequency of the electro-magnetic wave resonance occurs.

Answer 6

Good answers above for resonance. i have more to add regarding the radio.

A radio carrier wave is essentially a sin wave. It is modulated by multiplying it with the sound waves of the audio program you wish to transmit.

Lets say that the audio program is a simple sine wave tone of 256 cycles/sec. And let's say that the carrier wave is 580000 cycles/sec.

The cool thing about multiplying sine waves together is that you get another sine wave but at a different frequency.

In this case we would get 2 sine waves, one at 580256 cps and one at 579741 cps. To increase RF efficiency we can choose to only transmit the 580256 cps signal.

At the radio receiver we again multiply the received radio signal with our oscillator tuned to 580000 cps.
this will give us a pair of sin waves at 256 cps and at 1160256 cps. A simple filter is used to reject the larger frequency and we hear the original 256 cps tone.

now we can put in a much more complex signal than a simple tone and the result is that the output is the original radio program.

And it all works from a simple trigonometric identity.

sinA*sinB ="something like" sin(A+B) + sin(A-B)
I say "something like" since the real trig identities for adding angles or multiplying trig functions are a little more complex, but that is the general idea.

Answer 7

expect a long answer im too tired

Answer 8

because they have different physical properties!