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Q. 47

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 452

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Illustration

Short Answer

String 1 in FIGURE P16.47 has linear density 2.0 g/m and string 2 has linear density 4.0 g/m. A student sends pulses in both directions by quickly pulling up on the knot, then releasing it. What should the string lengths L1 and L2 be if the pulses are to reach the ends of the strings simultaneously?

and

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Step by Step Solution

Given information

The linear density of string 1 is

The linear density of string 2 is

Relationship between lengths of the two strings

Tension is the same in both the strings but wave speed is different.

Wave speed in string 1 is

Wave speed in string 2 is

But and and because the pulses are to reach the ends of the string simultaneously.

We have,

Length of the string 2

As

Substitute the given values

Therefore, the length of the string 2 is .

Length of the string 1

Substitute for into

Therefore, the length of the string 1 is .

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