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

[whoareyou]

Homework Statement

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

Homework Equations

The Attempt at a Solution

$\lambda_1f= \sqrt{\frac{\tau}{4\mu}}=\frac{1}{2}\sqrt{\frac{\tau}{\mu}}$
$\lambda_2f= \sqrt{\frac{\tau}{\mu}}$
$\therefore \lambda_1 = \frac{1}{2}\lambda_2$

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

 

[TSny]

That all looks correct to me.

 

[whoareyou]

Ok thanks. Its weird because the answer key says its D.