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The drawing shows two strings that have the same lengthand the same linear density. The left end of each string is attached to a wall,while the right

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asked 2021-03-21
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The drawing shows two strings that have the same lengthand the same linear density. The left end of each string is attached to a wall,while the right end passes over a pulley and is connected to objects of different weights(Wa and Wb). Different standing waves are set up on each string, but theirfrequencies are the same. If \(\displaystyle{W}_{{a}}={44}\ {N}\), what is \(\displaystyle{W}_{{b}}\).

Expert Answers (1)

2021-03-23

The drawing shows two strings that have the samelength and the same lineardensity. The left end of each string is attached to a wall, while the right end passes over a pulley and isconnected to objects of different weights (\(\displaystyle{W}_{{a}}\) and \(\displaystyle{W}_{{b}}\)). Different standing waves are set up on eachstring, but their frequenciesare the same.
If \(\displaystyle{W}_{{a}}={44}\ {N}\) what is \(\displaystyle{W}_{{b}}\) \(\displaystyle{\frac{{\lambda_{{a}}}}{{{2}}}}={l}\)
\(\lambda_a=2l\)
and \(\displaystyle\lambda_{{b}}=\lambda={l}\)
Since \(\displaystyle{V}=\lambda\cdot{v}=\sqrt{{{\frac{{{W}}}{{\mu}}}}}\) or \(\displaystyle\lambda={\frac{{{1}}}{{{\left({v}\right)}\sqrt{{{\frac{{{W}}}{{\mu}}}}}}}}\)
For first: \(\displaystyle\lambda_{{a}}={\frac{{{1}}}{{{\left({v}\right)}\sqrt{{{\frac{{{W}_{{a}}}}{{\mu}}}}}}}}\)
For second: \(\displaystyle\lambda_{{b}}={\frac{{{1}}}{{{\left({v}\right)}\sqrt{{{W}_{{b}}}}{\left\lbrace\mu\right\rbrace}}}}\)
Note: Rest of the parts are constant
\(\displaystyle{W}_{{b}}={\frac{{{W}_{{a}}}}{{{4}}}}\)
\(\displaystyle={\frac{{{44}}}{{{4}}}}\ {N}\)
\(\displaystyle{W}_{{b}}={11}{N}\)

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