As far as I know both are formed from interference of 2 waves. And why don't the stationary waves undergo destructive interference? It's a bit confusing.
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2 Answers
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Beat frequency is due to interference between two waves of different frequency, and is equal to the difference of the two frequencies.
When two waves of different frequency interfere, there are no stationary waves. Instead, the fringes in the interference pattern are constantly moving in such a way that if you put a tiny detector at a point in the interference pattern, it will observe peaks of intensity passing by at the beat frequency.
You might need to see a stationary wave to understand it. I You can find someone who plays a stringed instrument like a guitar, and ask them to show you how to play harmonics on a string. The point you touch to play any harmonic is a "node" - a place where two waves traveling in opposite directions always cancel out. If there are nodes, we call the wave pattern a "standing wave" or "stationary wave". There can only be nodes when the two waves have the same frequency. The two waves actually only need to overlap to form a stationary wave; they don't need to move in opposite directions.
There are many Youtube videos that illustrate standing/stationary waves, mostly showing waves moving in opposite directions; but all interference patterns consist of stationary waves formed by interference between overlapping waves of the same frequency.
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$\begingroup$ Mr. McGrew please clarify stationary waves. I am bit of struggling at this topic. $\endgroup$– GamiraCommented Jan 1, 2019 at 16:25
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$\begingroup$ OK, I edited my answer to explain stationary waves. $\endgroup$ Commented Jan 1, 2019 at 17:05
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$\begingroup$ Sir in most of the stuff I found on stationary waves showed two waves moving in opposite directions. So you are saying that it isn't actually important for the 2 waves to travel in opposite directions? $\endgroup$– GamiraCommented Jan 1, 2019 at 17:12
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$\begingroup$ That is right. Standing waves caused by waves moving in opposite directions are a special case of standing waves caused by waves overlapping in arbitrary directions. See [sites.ualberta.ca/~pogosyan/teaching/PHYS_130/FALL_2010/…. Directly between the two sources you can see the standing waves due to motion in opposite directions, and everywhere else you can see the same standing waves extending out to where the waves overlap but do not move in opposite directions. $\endgroup$ Commented Jan 1, 2019 at 17:22
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As a wave propagation is associated with energy transfer, in a standing wave pattern there is no energy transfer as the waves of same frequency travel in the opposite directions reflected from the surface of the same medium.