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121. Problem 17.29P (HRW) We consider the arrangement in which two strings of different linear mass density hold a mass through pulleys as shown in the figure 1. String 1 has linear density of 3.00 g/m and string 2 has a linear density of 5.00 g/m. They are under tension owing to the hanging block of mass M = 500 g. We have to calculate (a) the wave speed in each string. (b) In the situation when the block is divided into two blocks (with M = M1+M2 and the apparatus is rearranged as shown in the figure 2. We have to find M1 and M2 such that the wave speeds in the two strings are equal.
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Solution: Click For PDF Version (a) Speed of wave motion in a taut string is given be the relation
where T is the tension in the string and
In solving the first part of the problem we will use the following data Mass per unit length of string 1,
Mass per unit length of string 2,
Tension in each of the strings
Using the result that wave speed in a string,
we find that the wave speed in string 1
And , wave speed in string 2
(b) We next consider the situation when the block of mass 500 g is to be so divided into two pieces, which when hanged with strings 1 and 2 independently will result in equal wave speeds in both the strings. This is equivalent to the condition
We find,
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is its
mass per unit length.
and
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