Question

21.The extension in a string,obeying Hookeslaw is X.The speed of sound in the stretched string is V.If the external in the string is incresed to 1.5x the speed of the sound will be--------

Answer 1

$\begin{array}{l}\text{Let T be the initial tension on the string when extension is x}\\ \text{By Hooke's law}\\ T=kx\\ \text{Speed of sound on the string will be}\\ V=\sqrt{\frac{T}{m}}\\ \text{Let T' be the tension in the string when the string is stretched}\\ \text{to 1}\text{.5x}\\ T\text{'}=1.5kx\\ =>V=\sqrt{\frac{kx}{m}}\text{---1}\text{.}\\ \text{Speed of sound on the stretched string will be, assuming change in density}\\ \text{of the string due to the stretching is negligible}\text{.}\\ V\text{'}=\sqrt{\frac{1.5kx}{m}}\text{=}\sqrt{1.5}\sqrt{\frac{kx}{m}}\text{---2}\text{.}\\ \text{from eqn}\text{. 1}\\ V\text{'}=\sqrt{1.5}V\end{array}$