Why there is (2 * C)/L. I thought microwave is considered both ends closed so f

Question

Why there is (2 * C)/L. I thought microwave is considered both ends closed so fn = n* v/2L

A microwave oven works by producing standing waves of electromagnetic radiation inside a closed housing. Consider a microwave oven which is 30 cm wide and which has five standing wave nodes one at each end of the microwave plus three inside the oven itself. What does the frequency of the radiation need to be to produce this pattern? ANSWER: 2.0 x 10 Hz Why are real microwave ovens designed with 4 nodes instead of 3 or 5? Please Explain Expert Answer ila answered this Srinivas this answer helpful? 1 LKP o Was 127 answers f (2 C)/L (2 3*10n8)/(0.30) 2 1019 Hz

Explanation / Answer

SInce it is given the at start node is there and also at end so definately it is close end at both points so you are correct but since there are 5 nodes so in your formula you have to put n=4(if k nodes are there then n=k-1).Then you will get correct answer.

put n=4 ,frequency=n*v/2L=4*C/2L=2*10^9

you are also correct but method the person used was not clear so you were confused .

Another method (very basic method if you do not know even the formula)

Since it is given that 5 nodes are there (one at start,one at end and 3 midways)

so total cycles in a wave will be 2 cycles as if you draw two cycles with nodes starting from one end and also cycles ending with node(as said in the question itself) so you will get two complete cycles

means 2*wavelength=0.3

we got wavelength=0.3/2=0.15

frequency=speed/wavelength=3*10^8/0.15=2*10^9 Hz

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