A series of pulses, each of amplitude 0.190 m, are sent down a string that is attached to a post at one end. The pulses are reflected at the post and travel back along the string without loss of amplitude.
(a) What is the displacement at a point on the string where two pulses are crossing, if the string is rigidly attached to the post?
In this scenario, when two pulses cross at a point on the string that is rigidly attached to the post, the displacement at that point is the sum of the individual displacements of the two pulses.
Since each pulse has an amplitude of 0.190 m, and they are traveling in opposite directions (one pulse is moving towards the post and the other is moving away from the post), the displacement at the crossing point will be the algebraic sum of the two amplitudes.
If we choose the positive direction of displacement as the direction of the first pulse when it is moving away from the post, and the negative direction as the direction of the second pulse when it is moving towards the post, we can express the displacement at the crossing point as:
Displacement = Amplitude of the first pulse - Amplitude of the second pulse
Given that each pulse has an amplitude of 0.190 m, the displacement at the crossing point is:
Displacement = 0.190 m - (-0.190 m)
= 0.190 m + 0.190 m
= 0.380 m
Therefore, the displacement at a point on the string where two pulses are crossing, if the string is rigidly attached to the post, is 0.380 m.
To determine the displacement at the point where two pulses are crossing on a string that is rigidly attached to a post, we need to consider the principle of superposition.
The principle of superposition states that when two or more waves overlap, the resultant displacement at any point is the algebraic sum of the individual displacements produced by each wave.
In this case, we have two pulses traveling in opposite directions along the string. When they cross each other, they will overlap and interfere.
Assuming the pulses have the same amplitude and shape, we can say that they are identical. When the identical pulses meet, their algebraic sum will result in a displacement of zero at the point of intersection. This is because the two pulses will have equal but opposite displacements, canceling each other out.
Therefore, if the string is rigidly attached to the post, the displacement at the point where two pulses are crossing will be zero.