String 1 in the figure has linear density 2.70g/m and string 2 has linear densit

Question

String 1 in the figure has linear density 2.70g/m and string 2 has linear density 3.30g/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?

What should the string length L2 be?

String 1 in the figure has linear density 2.70g/m and string 2 has linear density 3.30g/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? What should the string length L2 be?

Explanation / Answer

The time taken to travel from the knot to the end of the string of length L1 is

t1 = L1/ sqrt (T/ m/L) = L1/ sqrt (T/ 2.7 * 10 ^-3 kg/m)

The time taken to travel from the knot to the end of the string of length L2 is

t2 = L2/ sqrt (T/ m/L) = L2/ sqrt ( T/3.3 * 10 ^-3 kg/m)

since t1 = t2

L1 sqrt 2.7 = L2 sqrt 3.3

1.643 L1 = 1.816 L2

since L1 + L2 = 4 m

L2 = 4m - L1

1.643 L1 = 1.816 ( 4 m- L1)

L1 = 2.1m

L2 = 4 m - 2.1m = 1.9 m

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