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

\(\displaystyle{W}_{{b}}={\frac{{{W}_{{a}}}}{{{4}}}}\)

\(\displaystyle={\frac{{{44}}}{{{4}}}}\ {N}\)

\(\displaystyle{W}_{{b}}={11}{N}\)