How Do Wave Pulses Behave at the Junction of Heavy and Light Springs?

[shadowice]

Homework Statement

Two springs are connected, one is a heavy spring and the other is a light spring. A pulse is traveling down spring A, towards a junction with spring B. Which of the following statements are correct/incorrect.

A. If spring A is the heavy spring then the transmitted pulse will not be inverted.
B. The only case in which there will be no reflected pulse is when the springs are identical.
C. If spring A is the heavy spring then the reflected pulse will travel slower than transmitted pulse.
D. If spring A is the light spring then the reflected pulse will be inverted.
E. If spring A is the light spring then the transmitted pulse will travel faster than reflected pulse.

The Attempt at a Solution

A. Correct
B. Correct
C. Incorrect
D. Correct
E. Correct

Im not really sure which is wrong

 

[anathema]

, but I think that C is incorrect. This is because the speed of a wave in a spring is determined by the properties of the medium, not the mass of the spring. Therefore, the transmitted and reflected pulses should travel at the same speed regardless of whether spring A is the heavy or light spring.

 

[nlightner]

or right.

I would like to clarify that the statements A, B, D, and E are correct while statement C is incorrect.

Firstly, the speed of a wave is determined by the properties of the medium it is traveling through, not by the weight of the spring. Therefore, the transmitted pulse will have the same speed regardless of whether spring A is heavy or light.

Secondly, when two identical springs are connected, there will be no change in the properties of the pulse as it travels from one spring to the other. This means that there will be no reflected pulse and the transmitted pulse will not be inverted.

Thirdly, when spring A is the light spring, the reflected pulse will be inverted. This is because the lighter spring will have a higher velocity and lower tension, causing the pulse to reflect with the opposite displacement.

Lastly, when spring A is the light spring, the transmitted pulse will travel faster than the reflected pulse. This is because the lighter spring has a higher velocity, allowing the pulse to travel faster.

In summary, the weight of the spring does not affect the speed of the pulse, but it does affect the inversion of the pulse and the speed of the transmitted pulse compared to the reflected pulse.