Two sinusoidal waves travel in the same direction

[blackout85]

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.


Help is appreciated

 

[anathema]

!

I would like to confirm that your answers are correct. In the first scenario, when two waves with the same frequency and opposite phases are superimposed, the resulting wave will have a smaller amplitude of Y1 + Y2. This is because the peaks of one wave will cancel out the troughs of the other wave, resulting in a smaller overall amplitude.

In the second scenario, the amount of energy carried by a wave is directly proportional to its amplitude. So if wave A has an amplitude twice that of wave B, it will also carry twice the amount of energy. This means that the rate at which energy is transmitted by wave A is also twice that of wave B. Therefore, the correct answer is b) twice.

I hope this helps clarify your understanding. Keep up the good work!

 

[m2003]

Your reasoning for the first question is correct. When two waves are 180 degrees out of phase, they will destructively interfere and cancel each other out, resulting in the smallest possible amplitude for the resultant wave.

For the second question, you are on the right track. The amplitude of a wave is directly proportional to the amount of energy it carries. So, if wave A has an amplitude that is twice that of wave B, it will carry twice as much energy. This means that the rate at which wave A transmits energy will also be twice that of wave B. Therefore, the correct answer is b) twice.