Two sinusoidal waves travel in the same direction and have the same frequency. Thier amplitudes are Y1 and Y2. The smallest possible amplitude of the resultant wave is:
a) Y1+Y2 and occurs if they are 180 degrees out of phase
b) [Y1-Y2] and occurs if they are 180 degrees out of phase
c) Y1 + Y2 and occurs if they are in phase
d) [y1-Y2] and occurs if they are in phase
e) [Y1-Y2] and occurs if they are 90 out of phase.
I think the answer would be A if Y1 +Y2 and they are 180 degrees out of phase. I choose the answer based on the fact that superposition is based on the Y1 +Y2= resultant. So if the waves were out of phase they would produce the smallest resultant because the other is the complete reverse of the other. I thinking deconstruction.
Two identical waves but separate string, with the same tension carry sinusoidal waves with the same frequency. Wave A has an amplitude that is twice that of wave B and transmits energy at a rate that is _____ that of wave B.
a) half
b) twice
c) one-fourth
d) four times
e) eight times
iI thought the answer would be B because the amount of energy carried by a wave is related to the amplitude of the wave. A high energy wave is characterized by a high amplitude; a low energy wave is characterized by a low amplitude. The amplitude of a wave refers to the maximum amount of displacement of a a particle on the medium from its rest position. The energy imparted to a pulse will only effect the amplitude of that pulse.
Thank you for any help.
Your reasoning on the first is exact, but the answers are sloppy written, I think b more closely fits your reasoning.
The second : energy is proportional to amplitude squared, so if one is double amplitude, it is four times as much energy.
Your reasoning for the first question is correct. When two sinusoidal waves have the same frequency and travel in the same direction, their amplitudes add up to give the resultant wave's amplitude. If they are 180 degrees out of phase (opposite in direction), then their amplitudes will add destructively, resulting in the smallest possible amplitude. Therefore, the answer is (b) [Y1 - Y2].
For the second question, you are correct that the energy carried by a wave is related to its amplitude. The energy is directly proportional to the square of the amplitude. In this case, if wave A has an amplitude that is twice that of wave B, then wave A will carry four times more energy than wave B. Therefore, the answer is (d) four times.