You and your friend are talking on a string telephone that is 14 m long. Each of you pulls on the string with about 9 N of force, meaning that the string tension is 9 N. The string has a mass density of 1.2 g/m. How long does it take for your voice to reach your friend through the telephone?
I tried to use this equation but I don't know if its the right equation and got confused
v=sqrt(tension force/mass per unit length)
you have the right formula, change g/m to kg/m
1.2g/m=.0012
v=sqrt(9/.0012)= about 86m/s
To determine the time it takes for your voice to reach your friend through the telephone, you need to consider the speed of sound in the string. The equation you mentioned, v = sqrt(tension force/mass per unit length), is close, but it is not the correct equation to use in this scenario.
In order to solve this problem, we need to consider the wave equation that relates the speed of sound in a medium to its tension and mass per unit length. The wave equation for a string is:
v = sqrt(F_T/(m/L))
Where:
v = speed of the wave (sound) in the string
F_T = tension force applied to the string
m/L = mass per unit length of the string
In this case, the tension force (F_T) is given as 9 N, and the mass per unit length (m/L) is given as 1.2 g/m. However, we need to convert the mass per unit length to kg/m to maintain consistent units.
Converting 1.2 g to kg:
1.2 g = 0.0012 kg (divide by 1000)
Now, we can substitute the given values into the equation:
v = sqrt(9 N / 0.0012 kg/m)
Simplifying further:
v = sqrt(7500 m^2/s^2) ≈ 86.6 m/s (approximately)
The speed of sound in the string is approximately 86.6 m/s.
To find the time it takes for the sound to travel through the string, we can use the formula:
time = distance / speed
The distance is given as 14 m (the length of the string), and the speed is approximately 86.6 m/s.
Plugging these values into the equation:
time = 14 m / (86.6 m/s) ≈ 0.162 s (approximately)
Therefore, it takes approximately 0.162 seconds for your voice to reach your friend through the string telephone.