Wave speed, tension, linear density

[sphouxay]

Homework Statement

The wave speed on a string is 155 m/s when the tension is 84.0 N.
What tension will give a speed of 182 m/s?

Homework Equations

velocity= Squareroot(tension/linear density)
linear density = mass/length

The Attempt at a Solution

Well, what I did was assuming that i just plug in the numbers my linear density would be 0.0035, my initial tension of 84 netted 155 m/s, I plugged this same number into find the tension with speed of 182 m/s and my answer was 115.934 after some manipulation of numbers, if this is correct is this answer already in N (Newtons).

 

[ponjavic]

As you solve for tension without manipulating the equations the answer is naturally in N.

 

[Mene]

Your approach is correct. The answer of 115.934 is in Newtons, as tension is typically measured in Newtons. It is important to note that the linear density of the string also affects the wave speed, so it is possible that the linear density may change in order to achieve a wave speed of 182 m/s. However, based on the given information, a tension of 115.934 N would result in a wave speed of 182 m/s. Keep in mind that this is an idealized situation and there may be other factors that could affect the wave speed in a real-world scenario.