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).

What is the ratio of v2:v1 (speed of the wave on string 2 to speed of the wave on string 1)?

What is the ratio of the mass densities of string 2: string 1?

Explanation / Answer

f = 3V1/2L1

f = 4V2/2L2

L1 = L2

4v2 = 3v1

v2/v1 = 3/4 <--------answer

v = sqrt(T/u)

Tension T is same

V2/v1 = sqrt(u1/u2)

u2/u1 = (v1/v2)^2 = 9/16 <--------answer

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