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Two transverse waveforms (A and B) travel through the same medium with a phase difference of 180°.  If the amplitude of the waveforms is ±100 m, what is the combined displacement of both waveforms as waveform A reaches maximum displacement?A.0 mB.100 mC.175 mD.200 m

Question

Two transverse waveforms (A and B) travel through the same medium with a phase difference of 180°.  If the amplitude of the waveforms is ±100 m, what is the combined displacement of both waveforms as waveform A reaches maximum displacement?A.0 mB.100 mC.175 mD.200 m

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Solution

The answer is A. 0 m.

Here's why:

  1. Transverse waves are waves in which the displacement of the medium is perpendicular to the direction of the wave.

  2. A phase difference of 180° means that one wave is half a cycle out of phase with the other. In other words, when one wave is at its maximum positive displacement, the other is at its maximum negative displacement.

  3. Given that the amplitude of the waveforms is ±100 m, this means that when waveform A is at its maximum displacement (+100 m), waveform B is at its maximum negative displacement (-100 m).

  4. The combined displacement of both waveforms is the sum of their individual displacements. So, when waveform A is at +100 m and waveform B is at -100 m, their combined displacement is 0 m.

Therefore, when waveform A reaches maximum displacement, the combined displacement of both waveforms is 0 m.

This problem has been solved

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