Two waves, both of amplitude A, are traveling in opposite directions along a rope. What is the range of displacement y that the two waves may cause when they overlap?
-2A <= y <= 2A
-A <= y <= A
-1/2A <= y <= 1/2A
0<= y <= A
A scientist rings a bell to study sound waves in a room. Which action will decrease the effect of overlapping sound waves in the room?
Lining the walls with material that reflects sound waves
Lining the walls with material that absorbs sound waves
Ringing several bells, each of different size
Ringing several identical bells at different times.
In a sinusidal standing wave, a node forms where superstition consistently causes______.
Maximum amplitude
Amplitude of one half maximum
Amplitude of one half the wavelength
Zero amplitude
Please help!
For the first question about the range of displacement caused by overlapping waves, the correct answer is:
-A <= y <= A
To understand why, we need to consider the interference of the waves. When two waves overlap, their displacements add up at each point along the rope. The maximum possible displacement occurs when the two waves are in phase and have the same amplitude, resulting in their displacements reinforcing each other. So, the maximum displacement is 2A (amplitude of one wave) + 2A (amplitude of the other wave) = 4A. Similarly, the minimum possible displacement occurs when the two waves are completely out of phase and cancel each other out, resulting in a displacement of -2A.
Hence, the correct range of displacement is -A <= y <= A.
For the second question, to decrease the effect of overlapping sound waves in a room, the appropriate action is:
Lining the walls with material that absorbs sound waves
When sound waves hit a surface, they can reflect, transmit, or be absorbed by the material of that surface. Reflecting surfaces can cause sound waves to bounce around and create strong overlapping waves, which can lead to echoes and reverberations. However, absorbing surfaces can reduce the reflections and dissipate the sound energy, thereby decreasing the effect of overlapping sound waves in the room.
So, the correct action is lining the walls with material that absorbs sound waves.
Finally, in a sinusoidal standing wave, a node is formed where destructive interference consistently causes:
Zero amplitude
In a standing wave, nodes are the points where the two traveling waves interfere destructively, resulting in no displacement or zero amplitude. At these nodes, the crest of one wave meets the trough of the other wave, canceling each other out and resulting in zero displacement.
Therefore, in a sinusoidal standing wave, nodes consistently exhibit zero amplitude.