The extension in a string obeying Hooke's law is $x.$ The speed of sound in the stretched string is $v.$ If the extension in the string is increased to $1.5x$, the speed of sound will be
IIT 1996, Diffcult
Download our app for free and get started
(a) Speed of sound in a stretched string $v = \sqrt {\frac{T}{\mu }} $…$(i)$
Where $T$ is the tension in the string and $\mu $ is mass per unit length.
According to Hooke’s law, $F \propto x$ $T \propto x$…$(ii)$
From $(i)$ and $(ii)$ $v \propto \sqrt x $ $\Rightarrow$ $v' = \sqrt {1.5} \;v = 1.22\;v$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1The transverse displacement $y(x, t)$ of a wave on a string is given by $y(x, t)=e^{-\left(a x^2+b t^2+2 \sqrt{a b} x t\right)}$ This represents aView Solution
- 2A surface of area $S$ is placed perpendicular to the direction of travel of a plane wave. The energy per unit time intercepted by the surface is $E$ when the amplitude of the wave is $A$ . The area of the surface is reduced to $\frac{1}{2} \ S$ and the amplitude of the wave is increased to $2\ A$ . What is the energy per unit time intercepted by this smaller surface?View Solution
- 3Figure given shows a sinusoidal wave on a string. If the frequency of the wave is $150\, Hz$, what is the wavelength and velocity of the given wave ?View Solution
- 4View SolutionWhich of the following statements is false
- 5Velocity of sound in vacuum is .... $ms^{-1}$View Solution
- 6View SolutionMaximum number of beats frequency heard by a human being is
- 7The sound intensity level at a point $4 \,m$ from the point source is $10 \,dB$, then the sound level at a distance $2 \,m$ from the same source will be ........ $dB$View Solution
- 8$Assertion :$ Sound waves cannot travel in vacuum but light can travel in vacuum.View Solution
$Reason :$ Sound waves are longitudinal waves and they cannot be polarised but electromagentic waves are transverse and they can be polarised. - 9View SolutionWhich of the following do not require medium for transmission
- 10If the velocity of sound in air is $336 m/s$. The maximum length of a closed pipe that would produce a just audible sound will beView Solution