Constructive and Destructive waves?

[stn1983]

Ok I came upon a question while studying for the Mcat, and I am having problems understanding how they got the answer.

Two mechanical waves of the same frequency pass through the same medium. The range of amplitudes possible when the two waves pass through the medium is between four and twelve. Which of the following describes the possible amplitudes of the two waves?

a)6 units and 2 units
b)8 units and 4 units
c)12 units and 4 units
d)10 units and 2 units

The answer is B, and their explanation to how they got the answer is:When maximum destructive interference occurs, amplitude = 8 - 4 = 4 units; when maximum constructive interference occurs, amplitude = 8 + 4 = 12 units, thus the range is between 4 and 12.

So my question is; for a maximum destructive interference wouldn't you take the minimum amplitude of each wave and take the sum of it? For example, the minimum amplitude of each wave is 4 units, therefore, the sum is 8 units. Vice versa, the maximum constructive interference is the summation of the maximum amplitude of each wave. In this case it's 12 units for each wave which equals 24 units.

Any help or explanation will be appreciated. Thank you

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[cwfergus]

Ok I came upon a question while studying for the Mcat, and I am having problems understanding how they got the answer.

Two mechanical waves of the same frequency pass through the same medium. The range of amplitudes possible when the two waves pass through the medium is between four and twelve. Which of the following describes the possible amplitudes of the two waves?

a)6 units and 2 units
b)8 units and 4 units
c)12 units and 4 units
d)10 units and 2 units

The answer is B, and their explanation to how they got the answer is:When maximum destructive interference occurs, amplitude = 8 - 4 = 4 units; when maximum constructive interference occurs, amplitude = 8 + 4 = 12 units, thus the range is between 4 and 12.

So my question is; for a maximum destructive interference wouldn't you take the minimum amplitude of each wave and take the sum of it? For example, the minimum amplitude of each wave is 4 units, therefore, the sum is 8 units. Vice versa, the maximum constructive interference is the summation of the maximum amplitude of each wave. In this case it's 12 units for each wave which equals 24 units.

Any help or explanation will be appreciated. Thank you

How is the minimum amplitude of each wave 4 units? It says right in the question that when Constructive interference occurs, it is 12 units and when destructive interference occurs it is 4 units. This means that when the two cross each other, it will either be 12 or 4. So you have to think first, "what is constructive interference?" and we know that it is the sum of the two waves at that point. So 'B' and 'D' are the only correct answers because they add up to give 12 units, which in the question, is what happens when constructive interference occurs. Now you have to think what destructive interference is which is the subtraction of the two amplitudes of the waves. So we know that it has to be 4 units, so what of 'B' and 'D' would give us 4 units if they are subtracted. Well that would just be 'B' because 'D' would give you an 8 unit destructive interference..

Im sorry, its hard to explain here.. drawing pictures might help though..