What does the frequency sharpness mean?

In summary, the frequency response measures the amplitude of an oscillation as it relates to the frequency, while the sharpness of resonance is determined by the Q factor which is related to how quickly the energy of the oscillating system decays. The shape of the resonance curve can be described using mathematical functions such as Gaussian or Lorentzian profiles, and the ratio of the maximum value to the Full width-Half maximum determines the Q value. Mechanical resonance peaks occur when there is a driving force and some damping present, and the amplitude of these peaks depends on the frequency of the driving force and the damping factor. The width of the resonance curve is equal to 1/Q, with higher Q values resulting in narrower peaks.
  • #1
apache
what does the 'frequency response' and 'sharpness' of resonance mean ?
thanks
-apache
 
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  • #2
Frequency response is a measure of the amplitude of an oscillation as a function of frequency.

Sharpness of resonance is defined by the Q factor, which is related to how quickly the energy of the oscillating system decays.
 
  • #3
thank you..
the frequency response would then be shown with the bell curve right ? with max. amplitude at the natural freq. of the system.
but what would be the determinants of the shapness of resonance?
thank you once again
-apache
 
  • #4
See here...

http://www.cims.nyu.edu/~barnett/tf/q.pdf
 
  • #5
Usually by bell curve they mean Gaussian profile exp(-f2). The resonance curve shape is 1/(1-f2) which is usually called Lorents curve.
 
  • #6
the frequency response would then be shown with the bell curve right

Magnitude vs. frequency is shown via Bode magnitude diagrams.

They do not always have a peak. It depends on the system dynamics.
 
  • #7
Apache,

The determinants of the sharpness in resonance depends on the system involved. Lots of physical systems undergo resonance peaks, in the case of inhomogenously broadened optical oscillators (lasers) for example, the sharpness depends on the losses in the cavity, the gain medium, the shape and reflectivity of the mirrors and the length of the cavity.

Resonance peaks can be described mathematically using Gaussian, Lorentzian or a combination between the two (convolution) called a Voight profile. All these mathematicals functions have 2 important parameters, the maximum value and the Full width-Half maximum (The width of the curve at 1/2 the maximum value.) The ratio of these two parameters gives the Q values. Tall skinny peaks have high a Q, flat broad peaks have a low Q.

As enigma correctly points out, there need not be a resonant peak at all. Indeed there may be many overlapping resonance peaks (common in the case of lasers).
 
  • #8
thanks for the replies,
yeah i was wrong on the bell curve lol .. but it kinda looks like a bell, with 0 gradient and max amplitude at f0 ...
anyhow.. i don't think i understand how the sharpness would be affected in mechanical SHM .. like mabye a spring and mass etc..
thanks for all your help
 
  • #9
Resonance peaks do not occur in Simple Harmonic oscillators, only in mechanical oscillators with some damping constant, r and some sinusoidal driving force, F(t).

The frequency of oscillation you get with SHM is called the natural resonance of the system, so called because it resonates at that frequency without a driving force (i.e. F(t)=0). For damped oscillators, the natural frequency is slightly different than that of an undamped system (i.e r=0, as in SHM).

It is possible to force an oscillator to oscillate at a frequency other than its natural frequency using a driving force, however the amplitude decreases. Plotting the driving force frequency vs amplitude will give a resonance peak.

Some characteristics of mechanical resonance peaks include:-
- Amplitude = F/s as w (drive frequency) approaches 0 (Hooke's Law)
- Amplitude approaches 0 as w approaches infinity.
 
  • #10
Resonance does occur in simple harmonic oscillator, resonance curve is then a delta-function (zero width and infinite amplitude).

Equation of forced oscillations in oscillating system can be written as: x"+(wo/Q)x'+wo2=wo2cos(wt), where wo is own (resonance) frequency of system and w - frequency of external force, 1/Q - damping factor (Q is usually called quality of oscillating system).

Stationary solution of this equation (established oscillations in such system after some time) is: x(t)=xocos(wt), where amplitude of oscillations depends on frequency w of external force: xo={[(1-(w/wo)2]2+(w/Qwo)2}-1

You may see that for ideal oscillator (Q=oo) amplitude xo becomes delta function. For non-infinite Q values the width of resonance curve deltaw/wo (FWHM = width on 1/2 level for energy = width on 0.71 level for amplitude) is equal to 1/Q.

Typical Q values: mass on spring 1-10, radio LC circuit 10-100, mass on a string 100-1000, quarts watch crystal 104-5, spectral lines (in visible range) 105-6, orbiting moons and planets 107-9, good laser 108-9, atomic clock cavity 1011-13.
 
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What does the frequency sharpness mean?

The frequency sharpness refers to the ability of a signal to differentiate between different frequencies. In other words, it measures how distinct or clear the individual frequencies are in a given signal.

How is frequency sharpness measured?

Frequency sharpness is typically measured using a metric called the critical bandwidth. This is the range of frequencies within which the human ear can differentiate between two different tones. The narrower the critical bandwidth, the sharper the frequency resolution.

What causes differences in frequency sharpness?

Frequency sharpness can vary due to a number of factors, including the physical characteristics of the sound source, the characteristics of the medium through which the sound is traveling, and the sensitivity of the human ear.

Why is frequency sharpness important in sound analysis?

Frequency sharpness is important in sound analysis because it allows us to distinguish between different sounds and determine their characteristics. It also plays a role in our perception of sound quality and can impact our ability to understand speech or music.

How can frequency sharpness be improved?

The sharpness of frequency can be improved through various methods, such as using advanced signal processing techniques, optimizing the design of sound-producing devices, and reducing background noise. Additionally, training and practice can improve a person's ability to differentiate between different frequencies in sound.

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