Solved: Pulse Wave Problem - Speed of the Crest in m/s

[bricker9236]

Homework Statement

A string of length l = 5 m weighs M = 10 kg . A pulse wave is traveling along the string. What is the speed v of the crest of the pulse, in the uint of m/s , if the tension of the string F is 200 N ?

Homework Equations

v= sqrt F/u
u= m/L

HELP: We can obtain an expression for the wave speed by analyzing the forces acting a string of length l and mass M. Do you recall the resulting relation between the speed of the wave and the tension and the linear density?

HELP: ...Get the density by defination and then use above equation.

The Attempt at a Solution

I tried importing the numbers into the equation what I thought was the equation the HELP statement suggested.. and i got

v=sqrt 200/(10/15) = 17.320 ... is there something else i should be doing because this answer was wrong but i thought for sure i was doing it correct.

 

[kuruman]

The length of the string is 5 m. Where did you get 15 m?

 

[kerimek]

I would approach this problem by first identifying the relevant equations and variables. In this case, the relevant equation is the wave speed equation, v=sqrt(F/u), where F is the tension in the string and u is the linear density (mass per unit length). The given variables are the length of the string (l=5m), the mass of the string (M=10kg), and the tension (F=200N).

Next, I would use the given information to calculate the linear density, u, by dividing the mass by the length of the string (u=M/l=10kg/5m=2kg/m). Then, I would plug in the values for F and u into the wave speed equation to solve for v: v=sqrt(200N/2kg/m)=20m/s. This would be the speed of the crest of the pulse in meters per second.

It is important to note that the units for the linear density must be in kilograms per meter (kg/m) in order for the final answer to be in meters per second (m/s). If the units are not consistent, the final answer will be incorrect.

In conclusion, the speed of the crest of the pulse in this problem is 20 m/s. It is important to carefully analyze the given information and use the correct equations and units to arrive at the correct solution.