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Yolanda is studying two waves. The first wave has an amplitude of 2 m, and the second has an amplitude of 3 m.
Which statement accurately describes something that Yolanda can do as a part of her study?
She can use destructive interference to generate a wave with an amplitude of 3.1 m.
She can use constructive interference to generate a wave with an amplitude of 1.5 m.
She can use destructive interference to generate a wave with an amplitude of 0 m.
She can use constructive interference to generate a wave with an amplitude of 3.5 m.
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Answer: She can use destructive interference to generate a wave with an amplitude of 3.1 m.
Reason: The resultant amplitude R of two waves (amplitudes 2 and 3) is R = sqrt(2^2 + 3^2 + 2·2·3·cosφ), so R ranges from |3−2| = 1 m (complete destructive) to 3+2 = 5 m (complete constructive). 3.1 m lies between 1 and 5 and corresponds to cosφ ≈ −0.282 (partially destructive), so it is achievable. The 0 m case is impossible (minimum is 1 m); 1.5 m would also require destructive, and 3.5 m cannot come from fully constructive interference.
Reason: The resultant amplitude R of two waves (amplitudes 2 and 3) is R = sqrt(2^2 + 3^2 + 2·2·3·cosφ), so R ranges from |3−2| = 1 m (complete destructive) to 3+2 = 5 m (complete constructive). 3.1 m lies between 1 and 5 and corresponds to cosφ ≈ −0.282 (partially destructive), so it is achievable. The 0 m case is impossible (minimum is 1 m); 1.5 m would also require destructive, and 3.5 m cannot come from fully constructive interference.
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