Write definition and dimensional formula of linear mass density of string.

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A sound is produced by plucking a string in a musical instrument, then

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by $4\, \%$, will be ......... $\%$

  • [JEE MAIN 2021]

Write equation of transverse wave speed for stretched string.

A steel wire has a length of $12.0 \;m$ and a mass of $2.10 \;kg .$ What should be the tension in the wire so that speed of a transverse wave on the wire equals the speed of sound in dry air at $20\,^{\circ} C =343\; m s ^{-1}$

A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $45 \;Hz$. The mass of the wire is $3.5 \times 10^{-2} \;kg$ and its linear mass density is $4.0 \times 10^{-2} \;kg m ^{-1} .$ What is

$(a) $ the speed of a transverse wave on the string, and

$(b)$ the tension in the string?