If tension in a wire is made four times, then what will be the change in speed of wave propagating in it ?
If tension in a wire is made four times, then what will be the change in speed of wave propagating in it ?
Wave speed in the wire is $v=\sqrt{\frac{\mathrm{T}}{\mu}}$
$\therefore \quad v \propto \sqrt{\mathrm{T}} \Rightarrow \frac{v_{1}}{v_{2}}=\sqrt{\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}}$
$\therefore \frac{v_{1}}{v_{2}}=\sqrt{\frac{\mathrm{T}_{1}}{4 \mathrm{~T}_{1}}} \Rightarrow v_{2}=2 v_{1}$
$\therefore$ Wave speed will become doubled.
Similar Questions
Write equation of transverse wave speed for stretched string.
Write equation of transverse wave speed for stretched string.
The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by $4\, \%$, will be ......... $\%$
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]
A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda _1$, is produced at the lower end of the rope. The wave length of the pulse when it reaches the top of the rope is $\lambda _2$. The ratio $\lambda _2\,/\,\lambda _1$ is
A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda _1$, is produced at the lower end of the rope. The wave length of the pulse when it reaches the top of the rope is $\lambda _2$. The ratio $\lambda _2\,/\,\lambda _1$ is
- [NEET 2016]
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 ......
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 ......
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 $...$
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 $...$
- [JEE MAIN 2022]