# Relationship between frequency and mass

### Q & A: mass and frequency | Department of Physics | University of Illinois at Urbana-Champaign

Answer the Question by describing the relationshipbetween frequency and amplitude, frequency and mass, and frequencyand length, both in words. Download scientific diagram | The relationship between mass and frequency change. from publication: Research and design of resonant mass sensor based on. Now you can figure out the frequency of a carbon 12 atom, remembering that Yes, so long as by "mass" you mean the inertial mass, the basic relation you.

I get a frequency of 2. Of course you may wonder what in the world we are talking about here- what's the 'frequency' of an atom? It's really a quantum mechanical property. Quantum mechanics allows systems to exist in a mixture of different states, all at the same time. If a system is prepared so that it is in a mixture of two different states with different frequencies, then some of the properties of the system will oscillate with a frequency that's the difference of the frequencies of the two ingredient states.

The common name for this is "beat frequencies". An example of this from particle physics is neutrino oscillation. Neutrinos come in three types, or "flavors" -- electron, muon, and tau. These we now know to have small masses which are different from each other.

### Proportionality between Frequency and Mass | Physics Forums

These small masses correspond to different frequencies according to your formula above. Neutrinos are made as an electron neutrino, a muon neutrino, or a tau neutrino, but these three states are mixtures of the states with definite mass, and so the neutrinos slowly oscillate from one flavor to another and back again as they travel through space. Measurements of this oscillation rate gives us indications about the differences of the masses of the neutrinos. Hi, I'm having difficulty reverse engineering this formula.

If we tap on the mass while it is in its equilibrium position, the oscillations begin. In words, the mass first moves away from equilibrium in one direction we'll call that the positive directionreaches a maximum displacement from equilibrium where it changes its direction of motion instantaneously coming to restspeeds up as it moves back towards the equilibrium position going in the opposite direction compared to when we tapped itslows down as it passes the equilibrium position until it reaches its maximum negative displacement the same distance from the origin as the maximum positive displacement and then heads back to the origin.

What we've described is one cycle of its oscillation. The oscillation cycles repeat. Quantitatively we can measure the time to complete one cycle. This is called the period of the motion generally abbreviated as T.

We could also count the number of cycles that occur in each second. That number, in general, will be a fraction: This measure is called the frequency of the motion abbreviated as f. These two measures of the motion are clearly interrelated: The units of f are cycles per second. In honor of Heinrich Hertz, we use the units of Hertz abbreviated Hz: We can also easily measure the maximum displacement of the mass in both the positive and negative directions. We find that both of these points are the same distance from the equilibrium position.

This quantity is called the amplitude of the motion. There is a simple correspondence between the terms we've used to describe simple harmonic oscillations and those we use to describe sound.

The frequency of oscillations is related to the pitch of sound. The amplitude of oscillation is related to the loudness of sound. We'll discuss this in more detail later in the semester.

Sound generally involves the superposition of many different pitches, corresponding to describing general oscillations as a superposition of simple oscillations at different frequencies. The motion of a simple harmonic oscillator is related to a pure tone single frequency in sound.

We can quantitatively measure the position of the mass versus time. Graphically, the position versus time looks like When working with the equation describing position versus time, we will end up dealing with trigonometric functions.

## Relationship between frequency and mass?

You might need to review them. Otherwise, you would be specifying an angle for the "sin" or "cos" function in degrees. In the above formula, the "angle" for the "sin" function has no units. It's because both t and the period T have units of seconds; this means their ratio has no units. An angle specified like this is said to be given in radians even though that's not really a physical unit.

You need to make sure you see "R" or "RAD" in your calculator's display. Bring it to my office if you need help setting it up! Oh yeah, there is another units conversion factor to convert an angle in radians to one in degrees.