Physics - Wave on String Question with Solution | TestHub

The frequency of a stretched string is given by $f=\frac{p}{2L}\sqrt{\frac{T}{\mu }}$

where $p$ is the number of antinodes (loops), $L$ is the length of the wire, $T$ is the tension, and $\mu$ is the linear mass density.

For the first case, $p_1=5$ and $T_1=9g$.

$f=\frac{5}{2L}\sqrt{\frac{9g}{\mu }}$

For the second case, $p_2=3$ and $T_2=Mg$.

$f=\frac{3}{2L}\sqrt{\frac{Mg}{\mu }}$

Since the wire resonates with the same tuning fork, the frequency $f$ remains constant. Equating the two expressions:

$\frac{5}{2L}\sqrt{\frac{9g}{\mu }}=\frac{3}{2L}\sqrt{\frac{Mg}{\mu }}$

$5\sqrt{9}=3\sqrt{M}$

$5\times 3=3\sqrt{M}$

$\sqrt{M}=5$

$M=25$ kg

Answer: $25$