The transverse displacement in a streched string is given by
$y = 0.06 \sin \, \left( {\frac{{2\pi }}{3}x} \right)\cos \,(120\pi t)$
$y = 0.06 \sin \, \left( {\frac{{2\pi }}{3}x} \right)\cos \,(120\pi t)$
where $x$ and $y$ are in $m$ and $t$ is in $s$. The length of the string is $1.5\, m$ and its mass is $3.0 \times 10^{-2} \,kg$, then tension in string is ..... $N$
Medium
Download our app for free and get started
$\omega=120 \pi, \mathrm{k}=\frac{2 \pi}{3}, \mathrm{v}=\frac{\omega}{\mathrm{x}}$
$\therefore \mathrm{v}=\frac{120 \pi}{2 \pi / 3}=180 \mathrm{\,m} / \mathrm{s}$
$\mathrm{T}=\mathrm{v}^{2} \mu=180 \times 180 \times \frac{3 \times 10^{-2}}{1.5}=648 \mathrm{\,N}$
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
- 1A plane progressive wave is given by $y=2 \cos 2 \pi(330 t-x) m$. The frequency of the wave is:View Solution
- 2The length of a sonometer wire tuned to a frequency of $250 Hz$ is $0.60$ metre. The frequency of tuning fork with which the vibrating wire will be in tune when the length is made $0.40$ metre is .... $Hz$View Solution
- 3View SolutionWhen two sound waves are superimposed, beats are produced when they have
- 4The expression $y = a\, sin\, bx\, sin\, \omega t$ represents a stationary wave. The distance between the consecutive nodes is equal toView Solution
- 5Ultrasonic signal sent from $SONAR$ returns to it after reflection from a rock after a lapse of $1 \,sec.$ If the velocity of ultrasound in water is $1600 ms^{-1}$, the depth of the rock in water is ..... $m$View Solution
- 6A bat moving at $10\,ms^{-1}$ towards a wall sends a sound signal of $8000\,Hz$ towards it. On reflection it hears a sound of frequency $f$. The value of $f$ in $Hz$ is close to (speed of sound $= 320\,ms^{-1}$ )View Solution
- 7$Assertion :$ The fundemental frequency of an open organ pipe increases as the temperature is increased.View Solution
$Reason :$ As the temperature increses, the velocity of sound increases more rapidly than length of the pipe. - 8View SolutionWhich of the following is the example of transverse wave
- 9A plane progressive wave is represented by the equation $y = 0.1\sin \left( {200\pi t - \frac{{20\pi x}}{{17}}} \right)$ where y is displacement in $m$, $ t$ in second and $x$ is distance from a fixed origin in meter. The frequency, wavelength and speed of the wave respectively areView Solution
- 10If the wave equation $y = 0.08\sin \frac{{2\pi }}{\lambda }(200t - x)$ then the velocity of the wave will beView Solution