A string of length $1 \mathrm{~m}$ and mass $2 \times 10^{-5} \mathrm{~kg}$ is under tension $\mathrm{T}$. when the string vibrates, two successive harmonics are found to occur at frequencies $750 \mathrm{~Hz}$ and $1000 \mathrm{~Hz}$. The value of tension $\mathrm{T}$ is. . . . . . .Newton.

Mechanical wave (sound wave) in a gas is

A transverse wave is passing through a string shown in figure. Mass density of the string is $1 \ kg/m^3$ and cross section area of string is $0.01\ m^2.$ Equation of wave in string is $y = 2sin (20t - 10x).$ The hanging mass is (in $kg$):-

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?

The speed of a transverse wave passing through a string of length $50 \;cm$ and mass $10\,g$ is $60\,ms ^{-1}$. The area of cross-section of the wire is $2.0\,mm ^{2}$ and its Young's modulus is $1.2 \times 10^{11}\,Nm ^{-2}$. The extension of the wire over its natural length due to its tension will be $x \times 10^{-5}\; m$. The value of $x$ is $...$

A pulse is generated at lower end of a hanging rope of uniform density and length $L$. The speed of the pulse when it reaches the mid point of rope is ......