Waves: finding the tension of a cord

In summary, the tension in the telephone cord is determined by the velocity (v) and mass per unit length (u), which are calculated using the distance (d) and time (t) for four trips down and back along the cord. The correct answer for the tension (T) is 18.2278N, which differs from the incorrect answer by orders of magnitude due to a mistake in calculation.
  • #1
nowtrams
5
0
1. A telephone cord is 3.95 m long and has a mass of 0.180 kg. A transverse pulse is produced by plucking one end of the taut cord. The pulse makes four trips down and back along the cord in 0.790 s. What is the tension in the cord?

d=3.95m, m=0.18kg, 4t=0.79s2.
v=(T/u)^0.5 --- v2=T/u --- T=v2*u

v=d/t

u=m/d

3.
4t = 0.79s
t = 0.79s/4 = 0.1975s

v = d/t = 3.95m/0.1975s = 20.0m/s

u = m/d = 0.18kg/3.95m = 0.0455696kg/m

T = v2*u = (20.0m/s)2*0.04557kg/m = 400m2/s2*0.04557kg/m = 18.2278481kg*m/s2
T = 18.2278N

this is from an electronic assignment and when I submitted this answer it said my answer "differs from the correct answer by 10% to 100%."
also, when I first attempted this problem I accidentally divided v2 by u instead of multiplying (which gave me 8777.778) and the response I got for that was that my answer differed from the correct answer by "orders of magnitude," which to me sounds like that answer was off by some multiple of 10.
 
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  • #2
Hi nowtrams, welcome to PF.
Four trips down and back means 4d or 8d?
 
  • #3
that's a good question, that hadn't occurred to me. I'll give that a try
 
  • #4
That was all my problem was, thanks!
 

FAQ: Waves: finding the tension of a cord

What is tension in a cord?

Tension is a force that is applied to an object by pulling on it. In the case of a cord, tension is the force that is exerted on the cord in order to keep it taut.

How do you find the tension of a cord?

The tension of a cord can be found using the formula T = F/l, where T is the tension in the cord, F is the force being applied to the cord, and l is the length of the cord.

What factors affect the tension of a cord?

The tension of a cord can be affected by factors such as the material of the cord, the amount of force being applied to the cord, and the length and thickness of the cord.

Why is it important to find the tension of a cord?

Knowing the tension of a cord is important in order to ensure that the cord can withstand the force being applied to it without breaking or stretching too much.

How can the tension of a cord be adjusted?

The tension of a cord can be adjusted by either increasing or decreasing the force being applied to the cord, or by changing the length or thickness of the cord.

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