Question

If you take 42.0 meters of string and ball it up and put it on a scale you measure that it weighs 18.8 grams. If you tighten a length of this same string to a tension of 8.5 Newtons, what is the wave speed for waves that would travel on this string when you plucked it?

Answer 1

The wave speed of the string can be calculated using the formula √(T/μ), where T is the tension and μ is the linear mass density. In this case, the wave speed is approximately 50.71 m/s.

Step-by-step explanation:

The wave speed of a string can be determined using the linear mass density and the tension in the string. The formula to calculate wave speed is given by:

Wave speed (v) = √(T/μ)

Where T is the tension in the string and μ is the linear mass density.

In this case, the tension of the string is 8.5 N and the linear mass density can be calculated by dividing the weight of the string by its length. So, the wave speed would be:

Wave speed = √(8.5 N / (0.0188 kg * 42.0 m))

Simplifying the equation, you would find:

Wave speed ≈ 50.71 m/s

Answer 2

137.74 m/s

Step-by-step explanation:

`L` = length of the string = 42 m

`m` = mass of the string = 18.8 g = 0.0188 kg

Linear mass density is given as

`\mu =(m)/(L)`

`\mu =(0.0188)/(42)`

`\mu` = 0.000448 kg/m

`v` = wave speed

`T` = Tension force in the string = 8.5 N

Wave speed is given as

`v = \sqrt{(T)/(\mu )}`

`v = \sqrt{(8.5)/(0.000448 )}`

`v` = 137.74 m/s