To analyze Yolanda's options regarding wave interference, let's look at the concepts of constructive and destructive interference:
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Constructive Interference occurs when two waves meet in phase and their amplitudes add together. The maximum amplitude obtainable through constructive interference, given the amplitudes of the two waves (2 m and 3 m), would be: \[ \text{Maximum amplitude} = 2 , \text{m} + 3 , \text{m} = 5 , \text{m} \]
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Destructive Interference occurs when two waves meet out of phase, causing their amplitudes to reduce. The minimum amplitude, when both waves are perfectly out of phase, would be: \[ \text{Minimum amplitude} = |3 , \text{m} - 2 , \text{m}| = 1 , \text{m} \] The amplitude can go to 0 m only if the two waves are equal in amplitude and perfectly out of phase.
Now, let's evaluate the given statements:
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She can use destructive interference to generate a wave with an amplitude of 3.1 m.
- This is not possible because destructive interference can only reduce the amplitude to a maximum of 1 m (not achieve 3.1 m).
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She can use constructive interference to generate a wave with an amplitude of 1.5 m.
- This is also not possible with constructive interference, as it can only increase the amplitude, not yield a lower amplitude than both individual waves.
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She can use destructive interference to generate a wave with an amplitude of 0 m.
- This is only possible if two waves of equal amplitude (3 m and 3 m or 2 m and 2 m) meet perfectly out of phase. Since she is working with amplitudes of 2 m and 3 m, she cannot achieve 0 m.
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She can use constructive interference to generate a wave with an amplitude of 3.5 m.
- This is feasible because constructive interference of a wave of amplitude 2 m and another of amplitude 3 m could result in an amplitude between the sum (5 m) and the differences (1 m). Achieving 3.5 m is possible within that range.
Thus, the correct statement is: She can use constructive interference to generate a wave with an amplitude of 3.5 m.