Finding speed of a string given length, mass, and velocity of wave

[mandy9008]

Homework Statement

A string is 50.0 cm long and has a mass of 3.0 g. A wave travels at 5.0 m/s along the string. A second string has the same length, but half of the mass of the first. If the two strings are under the same tension, what is the speed of the second string?

The Attempt at a Solution

I don't know which equation to start with. I tried to find omega (w) using w=sqrt(g/l) and then using v=wrt. I don't think this is right. Can someone point me in the right direction?

 

[darkys]

The correct equation is v=sqrt(T/μ), where T is the tension and μ is the linear mass density (mass divided by length). In this problem, the linear mass density of the two strings is different, so the velocity of the second string will be different. The linear mass density of the first string is 3.0 g/50.0 cm = 0.06 g/cm. The linear mass density of the second string is half of that, so it is 0.03 g/cm. Plugging these values into the equation, we get v = sqrt(T/0.03 g/cm) = sqrt(T/0.03) m/s. Since we know the tension is the same in both strings, the speed of the second string will also be the same, 5.0 m/s.