# 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 λ_{2} = 2λ_{1}?

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