TBR physics phase II passage III

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This passage is about wave speed and presents a setup with a wire tied down at two ends, where halfway down the wire, the material changes so that the mass per unit length value is different.
Question number 15 asks, "how does the tension in segment 1 compare with the tension in segment 2, if segment 1 is made of a denser material?"
A. segment 1 is under more tension
B. segment 2 is under more tension
C. Both are under equal tension


I reasoned that, since segment 1 has a denser material and thus a larger value for u:

v = square root of Tension/u


The tension in segment 1 must be greater, choice A. I said this because I assumed that the velocity of a wave pulse must be constant as it crosses the interface between the two materials, and thus the tension must change with the u value.


However, in their answer, they said that both segments are under equal tension. "If the tensions are different, there will be a net force on the interface, and it will deform over time....If there is a net force (F=ma), the interface will accelerate."

Would someone be kind enough to clarify this for me/point out why I am wrong?

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If you have a stationary beam being pulled on both ends, the tension throughout the entire beam needs to be the same to keep the beam from moving. If for example the tension was higher on the left side of the beam, the beam would need to be stretching or moving. In tug of war, for the rope to stay stationary, both sides need to pull the same amount (and this same tension needs to be constant throughout the rope).

The wave speed actually can change with density.
 
If you have a stationary beam being pulled on both ends, the tension throughout the entire beam needs to be the same to keep the beam from moving. If for example the tension was higher on the left side of the beam, the beam would need to be stretching or moving. In tug of war, for the rope to stay stationary, both sides need to pull the same amount (and this same tension needs to be constant throughout the rope).

The wave speed actually can change with density.

btw, didnt read the entire question, but it depends on the wave, only sound wave's speed depends on density. The speed of a transverse wave does depend on linear density and Tension.

Op, do you mind posting a picture?
 
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