String 1 in the figure has linear density 2.80 g / m and string 2 has linear den
ID: 2265506 • Letter: S
Question
String 1 in the figure has linear density 2.80g/mand string 2 has linear density 3.10g/m . A student sends pulses in both directions by quickly pulling up on the knot, then releasing it. Consider the pulses are to reach the ends of the strings simultaneously.
(Figure 1)
What should the string length L1 be?
L2?
String 1 in the figure has linear density 2.80g/mand string 2 has linear density 3.10g/m . A student sends pulses in both directions by quickly pulling up on the knot, then releasing it. Consider the pulses are to reach the ends of the strings simultaneously. What should the string length L1 be? L2?Explanation / Answer
Start with the fact that the time for each pulse is the same for both sections of string. Velocity for string one is:
v? = L? / t
Then using the equation for the speed of a wave on a string, we can write:
L? / t = ?[F / ??]
Solved for t:
t = L? / ?[F / ??]-------------->(1)
Similarly, the time for the pulse on the other part of the string is:
t = L? / ?[F / ??]-------------->(2)
The length of either section of string may be expressed in terms of the other, so:
L? = 4.0m - L?----------------->(3)
Setting (1) and (2) equal and subbing in (3), you get the quadratic equation (note that you have to also plug in the given values for ?? and ?? and that the tensions F are the same and divide out):
(1.5)L?