What would happen if two waves with different frequency were to pass through 1 point in space at the same time? Would they interfere at that point in space? Are superposition and interference the same thing?
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2 Answers
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No. In general, only linear waves (i.e. only waves described by a linear differential equation.) will superpose (in the usual sense of the word.) By linearity, the sum of two solutions is also a solution. Besides the common wave equation $$ \frac{\partial^2 u}{\partial t^2}=v^2 \nabla^2u $$ the Schrodinger equation is also linear. The combination of (linear) waves with different frequencies gives rise to beats (accoustic or otherwise).
This does not hold for non-linear waves, since in general the sum of two solutions is NOT a solution to the non-linear wave equation. A famous example of a non-linear wave equation is the Korteweg-de Vries equation, which will exhibit soliton (or solitary wave) solutions. In particular, the ``collision'' of two solitons does not result in interference.
Another example of a non-linear wave common in physics is the non-linear Schrodinger equation, which is used for instance in optical fibers.
answered Mar 30, 2018 at 17:24
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$\begingroup$ Would two linear waves that are causing a disturbance in the same thing(field, particles etc.) have their disturbances add up if they are passing through the same point in that thing(field, particles etc.) at the same time? For example, What would be the total disturbance in the EM field at a point if red and blue light were passing through it at the same time? Would it be the disturbance by red light + the disturbance by blue light? $\endgroup$– user190174Commented Mar 31, 2018 at 8:50
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Superposition is just adding the waves together. So if you have waves $w_1(x,t)$ and $w_2(x,t)$ then the superposition of them is just $w(x,t)=w_1(x,t)+w_2(x,t)$
Typically you hear of either constructive or destructive interference with waves of the same frequency where, at a point in space, the superposition is either at a maximum or 0. If they have different frequencies then you would probably get more of a beat frequency equal to the difference in the two individual frequencies.
answered Mar 30, 2018 at 13:38
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$\begingroup$ Would the Resultant wave of two waves with different frequencies even have a defined frequency? Frequency is defined as the time between two consecutive troughs. Maybe it has a frequency but it is constantly changing? $\endgroup$– user190174Commented Mar 30, 2018 at 13:42
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$\begingroup$ @ArjunNigam have a look here for two frequency acs.psu.edu/drussell/demos/superposition/superposition.html $\endgroup$– anna vCommented Mar 30, 2018 at 14:07
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$\begingroup$ What if the amplitudes are different? $\endgroup$– user190174Commented Mar 30, 2018 at 14:14