You have two string segments of equal length, and string 2 is heavier (higher ma

Question

You have two string segments of equal length, and string 2 is heavier (higher mass density) than string 1. You splice them together and fix the ends to two posts. You then drive the combo rope at some frequency (the frequency is the same for both halves of the combo rope!). You set up a standing wave that has this pattern: nodes at the splice and where each segment is attached to its pole plus two more nodes in one of the segments and three more nodes in the other segment (8 nodes in all).

Draw the standing wave pattern, with string 1 on the left and string 2 on the right. To do this, you need to decide which one will have more nodes and justify your answer.

Explanation / Answer

The velocity of the wave will be faster on the string 1, as it is lighter.

As the frequency is the same, then the wavelength on the lighter rope is longer.

Thus, string 1 has fewer nodes!

Thus, string 1 has 2 nodes, string 2 has 3 nodes.

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