interference is happened when addition of other frequencies

example: f1=50(Hz) f2=50(Hz)

if both interference with each other it will become 100(Hz)

Any two waves can interfere to give you a resultant amplitude (algebraic sum of the two individual waves which may differ in amplitude, frequency or phase) and thus giving a resultant intensity. Interesting results which stay as maxima or minima of intensity are observed only if the two interfering waves are coherent or have no phase or a constant defined phase difference which you can control by introducing longer or shorter paths. Any two waves will interfere with random phase differences and the interference effects would average out to nothing.

When you add displacements, the frequencies do not add as you mention. Do a simple algebraic addition of two sinusoidal waves of same amplitude and phase different and see what you get the resultant wave as.

Superposition (addition) of any number of harmonic (sinusoidal) waves (signals) of a given frequency which travel (propagate) in the same direction yields a harmonic wave of that same frequency. So, superposition of two (three, four, etc.) waves of 50 Hz yields a harmonic (sinusoidal) wave of the same frequency, 50 Hz. In this case, the resultant amplitude doubles (triples, quadruplicates, etc.) if the waves are of the same amplitudes and in-phase, and that is called constructive interference. When the waves are out-of-phase, the amplitude of resultant wave can be less than amplitude of either wave, alone, or can even be zero, and this is called destructive interference.

At any event where two or more waves overlap, they superimpose. I guess you ask if they also interfere: this requires high level of coherence and same state of polarization, so one can detect the interference pattern. in case you ask if they can overlap in space for long distance: this depends on the beam divergence and spot size properties. Different beams will never overlap forever. It is either near the source, or, far from it, that diffraction will take over and separate the beams, unless some kind of "wise" overlap is used (see beam combining term).

Signals at different frequencies also superpose.

Just plot a function sin (\pi t) + sin (2\pi t) and you will see the resulting signal.

Strictly speaking all signals in the same medium superpose.The resulting signals depends on many parameters as discussed above but in principle you can always write it down as a sum of of the individual contributions as long as you make sure you have the same reference time or so. This is possible because air/vacuum is linear medium so you simply perform linear superposition. (note that not all media are linear!)

In the air around you, you have a pretty big mess of signals!

However, in communications the trick is to make sure that you pick up the right signal. So the signals are designed so that they do not interfere with each other. For instance strictly speaking signals at 2.4 and 5.7 GHz do superimpose in the air but a receiver filters out the unwanted frequency band, i.e. antennas and filters make sure the unwanted signal is blocked. This is pretty much the principle of Frequency division multiple access (FDMA) where each user has a different frequency.

You can also use different techniques of multiple access. For instance TDMA (time division) where each user can only use an allocated slot. This is in GSM - so the basestation receives superposition signals from multiple users but by time gating it makes sure the date is recovered correctly.

Another alternative is Code Division Multiple Access (CDMA) where each user has its own code and the codes are mutually orthogonal. Then you see a superposition of signals from all users as they share the same band and share the same timeslot but with the unique code you suppress the unwanted users.

The last option is Spatial multiplex where you use antenna array to make direct signals to the users which are in different positions.

(hope this is helpful and not getting too far away from the topic you actually asked)

ELECTROMAGNETIC INTERFERENCE

Governments regulate the amount of radio-frequency (RF) interference that equipment can produce so that computers and televisions, for example, do not interfere with each other:

Several terms are important dealing with this subject:

– EMI, or electromagnetic interference, is the production of unwanted RF energy,

– EMC, or electromagnetic compatibility, is the ability of two or more devices to work together without interfering with one another.

– Susceptibility is a measure of a device’s sensitivity to external interference. Because a good receiving antenna is a good transmitting antenna, devices with high susceptibility are usually devices that generate EMI.

Suppression, or source suppression, is the preferred way of reducing EMI. This means that the source of RF energy has somehow been turned off or reduced. Containment, which is confining the energy inside some enclosure, is the next best strategy.

Energy that is dispersed through radio waves in air is radiated emission. The opposite type, conducted through power lines and cables, is conducted emission.

Government regulation is monitored through regulatory agencies. In the United States, the regulatory agency is the Federal Communications Commission, or FCC. The regulation dealing with computer-generated EMI not only specifies the amount of EMI that is acceptable but also the testing methods used to measure EMI. Testing and approval is usually done by private companies authorized to perform, testing.

For there to be an EMI problem there must be: (1) a source of RF power, such as a digital device, (2) coupling via a “transmission line” to (3) a radiating structure or “antenna”.

(Samuel H. Russ “Electromagnetic Effects in High-Speed Digital Systems”. In: John Kraus and Daniel A. Fleisch: ELECTROMAGNETICS with Applications, McGraw-Hill, 1999)

Electromagnetic Interference (EMI) can cause troubles in some equipment in airplanes and airports and in hospitals, and in implanted electronic medical devices (pacemakers, defibrillators neurostimulators).