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somecelxis
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Homework Statement
please refer to the notes , since we know that a cycle of cosine is as in the photo 1 , why the beat period has 8 complete cycle of cosine?
Pick a point where the sum has maximum magnitude. Here the two sources are 'in phase'. Go along to the next cycle of one of them. The two are now slightly out of phase. Each additional cycle you move along, the phase difference increases. The closer the two sources are in frequency, the smaller the phase shift each cycle, so the more cycles you have to go through for the phase difference to reach 2π (or thereabouts). When the phase shift reaches that value, the two are in phase again. That completes one beat.somecelxis said:why The closer they are to being identical the longer and more cycles it takes. In this case it takes 8 cycles.
? can you please explain further?
haruspex said:Pick a point where the sum has maximum magnitude. Here the two sources are 'in phase'. Go along to the next cycle of one of them. The two are now slightly out of phase. Each additional cycle you move along, the phase difference increases. The closer the two sources are in frequency, the smaller the phase shift each cycle, so the more cycles you have to go through for the phase difference to reach 2π (or thereabouts). When the phase shift reaches that value, the two are in phase again. That completes one beat.
somecelxis said:what do you mean by The two are now slightly out of phase. Each additional cycle you move along, the phase difference increases. The closer the two sources are in frequency, the smaller the phase shift each cycle,
do you mean pick 2 points on the graph of resultant displacement? how can two of them are sligtly out of phase?
In your diagram, the two sources are not shown.Go along to the next cycle of one of [the two sources]
haruspex said:No, I wrote
In your diagram, the two sources are not shown.
somecelxis said:i think i got what do you mean . based on the diagram , can i say that at 0.5T , the both grpah with f1 and f2 in phase again? whereas at T , both the graph is out of phase again? (180 degree difference)
The beat period is the time it takes for two waves with slightly different frequencies to produce a pattern of constructive and destructive interference. This phenomenon is known as a beat.
The beat period is calculated by taking the reciprocal of the difference between the two frequencies of the waves. In other words, it can be calculated as 1/Δf, where Δf is the difference between the two frequencies.
Beat frequency is the number of beats produced per second when two waves with slightly different frequencies interfere with each other. It is measured in Hertz (Hz).
Beat frequency and beat period are inversely related. This means that as the beat frequency increases, the beat period decreases, and vice versa.
A common example of beat period and beat frequency is the sound produced when tuning two musical instruments to the same note. Another example is the interference of radio waves with different frequencies, which can cause static or distortion in the signal.