Answer the questions using the simulation above Set the frequency of wave 1 to 428 Hz and the frequency of wave 2 to 436 Hz. (a) Waves 1 and 2 are precisely in phase with one another at t = 0. If you look at the sum of the two waves, you can see that the amplitude of their sum drops to zero at one particular time between 50 and 100 ms (there are lots of places where the sum is zero, but only one place where the envelope enclosing the fast oscillations is zero, and that's the point we're interested in). Precisely when is the time, between 50 and 100 ms, when the amplitude of the sum is zero? (b) How many periods does this time correspond to for wave 1? You can get a pretty accurate idea of this by counting peaks on the wave 1 graph, but you should calculate it accurately. (c) How many periods does this time correspond to for wave 2? Note the difference between your answers for parts (b) and (c). It should be exactly half a period, which is why the waves experience completely destructive interference at this time. Something to think about: see if you can come up with a general condition for the times when the sum of the two waves is a maximum, and a general condition for the times when the sum of the two waves is a minimum.
Answer the questions using the simulation above
Set the frequency of wave 1 to 428 Hz and the frequency of wave 2 to 436 Hz.
(a) Waves 1 and 2 are precisely in phase with one another at t = 0. If you look at the sum of the two waves, you can see that the amplitude of their sum drops to zero at one particular time between 50 and 100 ms (there are lots of places where the sum is zero, but only one place where the envelope enclosing the fast oscillations is zero, and that's the point we're interested in). Precisely when is the time, between 50 and 100 ms, when the amplitude of the sum is zero?
(b) How many periods does this time correspond to for wave 1? You can get a pretty accurate idea of this by counting peaks on the wave 1 graph, but you should calculate it accurately.
(c) How many periods does this time correspond to for wave 2?
Note the difference between your answers for parts (b) and (c). It should be exactly half a period, which is why the waves experience completely destructive interference at this time. Something to think about: see if you can come up with a general condition for the times when the sum of the two waves is a maximum, and a general condition for the times when the sum of the two waves is a minimum.
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