Waves MC Question – 2 strings, same tension, different μ

1. The problem statement, all variables and given/known data

A long string is constructed by joining the ends of two shorter strings. The tension in the strings
is the same but string I has 4 times the linear mass density of string II. When a sinusoidal
wave passes from string I to string II:

A. the frequency decreases by a factor of 4
B. the frequency decreases by a factor of 2
C. the wavelength decreases by a factor of 4
D. the wavelength decreases by a factor of 2
E. the wavelength increases by a factor of 2

2. Relevant equations

3. The attempt at a solution

[itex]\lambda_1f= \sqrt{\frac{\tau}{4\mu}}=\frac{1}{2}\sqrt{\frac{\tau}{\mu}}[/itex]
[itex]\lambda_2f= \sqrt{\frac{\tau}{\mu}}[/itex]
[itex]\therefore \lambda_1 = \frac{1}{2}\lambda_2[/itex]

So shouldn’t the answer be E since λ2 = 2λ1?

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