mass m=2 kg

length of the cord L = 2 m

(a) frequency in above situation F = 145 Hz

F = 6 * fundamental frequency since we have sixloops

=6f

i.e., 6f = 145 Hz

f = 24.16667 Hz

fundamental frequency f = 24.16667 Hz

\(\displaystyle{\left({\frac{{{1}}}{{{2}{L}}}}\right)}\sqrt{{{\frac{{{T}}}{{\mu}}}}}={24.16667}{H}{z}\)

where T= tension in the string = m g

substitute values we get linear density \(\displaystyle\mu\) value

( b ) .fundamental frequency \(\displaystyle{f}={\left({\frac{{{1}}}{{{2}{L}}}}\right)}\sqrt{{{\frac{{{T}}}{{\mu}}}}}\)

\(\displaystyle={\left({\frac{{{1}}}{{{2}{L}}}}\right)}\sqrt{{{\frac{{{m}{g}}}{{\mu}}}}}\)

\(\displaystyle{\frac{{{f}_{{1}}}}{{{f}_{{2}}}}}=\sqrt{{{\frac{{{m}_{{1}}}}{{{m}_{{2}}}}}}}\)

we know \(\displaystyle{f}_{{1}}={24.16667}\) Hz

\(\displaystyle{m}_{{1}}={2}\) kg

\(\displaystyle{m}_{{2}}={2.88}\)

from above equation we find f 2 value

( c) .similar procedure as problem ( b )

length of the cord L = 2 m

(a) frequency in above situation F = 145 Hz

F = 6 * fundamental frequency since we have sixloops

=6f

i.e., 6f = 145 Hz

f = 24.16667 Hz

fundamental frequency f = 24.16667 Hz

\(\displaystyle{\left({\frac{{{1}}}{{{2}{L}}}}\right)}\sqrt{{{\frac{{{T}}}{{\mu}}}}}={24.16667}{H}{z}\)

where T= tension in the string = m g

substitute values we get linear density \(\displaystyle\mu\) value

( b ) .fundamental frequency \(\displaystyle{f}={\left({\frac{{{1}}}{{{2}{L}}}}\right)}\sqrt{{{\frac{{{T}}}{{\mu}}}}}\)

\(\displaystyle={\left({\frac{{{1}}}{{{2}{L}}}}\right)}\sqrt{{{\frac{{{m}{g}}}{{\mu}}}}}\)

\(\displaystyle{\frac{{{f}_{{1}}}}{{{f}_{{2}}}}}=\sqrt{{{\frac{{{m}_{{1}}}}{{{m}_{{2}}}}}}}\)

we know \(\displaystyle{f}_{{1}}={24.16667}\) Hz

\(\displaystyle{m}_{{1}}={2}\) kg

\(\displaystyle{m}_{{2}}={2.88}\)

from above equation we find f 2 value

( c) .similar procedure as problem ( b )