A string has a tension of 100.0 N and a wave speed of40.0 m/s when it is plucked. What is the linear densityof the string?
Question
A string has a tension of 100.0 N and a wave speed of40.0 m/s when it is plucked. What is the linear densityof the string?
Solution
The wave speed v on a stretched string depends on the tension F and the linear mass density μ (mass/length) of the string. This relationship is given by the formula:
v = sqrt(F/μ)
We can rearrange this formula to solve for the linear density μ:
μ = F/v²
Given that the tension F is 100.0 N and the wave speed v is 40.0 m/s, we can substitute these values into the formula:
μ = 100.0 N / (40.0 m/s)²
μ = 100.0 N / 1600 m²/s²
μ = 0.0625 kg/m
So, the linear density of the string is 0.0625 kg/m.
Similar Questions
A string of mass 2000g and length 100metres is under tension of 150N. (i) Determine the linear density of the string (iii) Velocity of wave in the stringa.0.02N/M (ii) 0.866m/sb.0.03N/M (ii) 8.86m/sc.0.2N/M (ii) 0.866m/sd.0.02N/M (ii) 8.00m/se.0.4N/M (ii) 8.00m/sf.0.4N/M (ii) 0.0866m/s
The linear density of a vibrating string is 10−4kg/m. A transverse wave is propagating on the string, which is described by the equation y = 0.02 sin (x + 30 t), where x and y are in meters and time t in seconds. Then tension in the string is
"Linear density of a string is 1.5×10^(-4) kg/m and the wave equation is y=0.021sin(x+30t). Find the tension in the string where x is in meters and t is in seconds.
For the wave in the previous question, that was moving at 250250 m/s up, if the tension in the string is 15001500 N, what is the linear mass density of the string in kg/m?
A string has a mass of 0.180 kg and a length of 1.60 m.What is the linear density, m, of the string?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.