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

• whoareyou
In summary, when a sinusoidal wave passes from a string with 4 times the linear mass density to a string with normal linear mass density, the wavelength decreases by a factor of 2. This is because the tension is the same in both strings, but the linear mass density affects the relationship between wavelength and frequency.
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

## 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?

That all looks correct to me.

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

## 1. What is the relationship between tension and wave speed in two strings with different coefficients of friction?

The wave speed is directly proportional to the square root of tension and inversely proportional to the square root of the coefficient of friction. This means that as tension increases, the wave speed increases, and as the coefficient of friction increases, the wave speed decreases.

## 2. How does the coefficient of friction affect the amplitude of the wave?

The coefficient of friction does not directly affect the amplitude of the wave. However, it can affect the energy dissipation of the wave, which can lead to a decrease in amplitude over time.

## 3. Does the wavelength change when two strings with different coefficients of friction are under the same tension?

No, the wavelength is determined by the tension and mass per unit length of the string, not the coefficient of friction. As long as these values remain constant, the wavelength will also remain constant.

## 4. Can the wave speed be the same in two strings with different coefficients of friction?

Yes, the wave speed can be the same as long as the tension and mass per unit length of the strings are also the same. The coefficient of friction does not directly affect the wave speed, but it can affect the energy dissipation of the wave.

## 5. How does the frequency of the wave change when the coefficient of friction is altered?

The frequency of the wave does not change when the coefficient of friction is altered. The frequency is determined by the source of the wave and the properties of the medium, not the coefficient of friction.

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