Calculate the frequency of the second harmonic formed on a string of length $0.5 m$ and mass $2 × 10^{-4}$ kg when stretched with a tension of $20 N$ …. $Hz$

A $43\, m$ long rope of mass $5.0\, kg$ joins two rock climbers. One climber strikes the  rope and the second one feels the effect $1.4\, s$ later. What is the tension in the rope …. $N$ ?

The transverse displacement of a string (clamped at its both ends) is given by

$y(x,t)\, = \,0.6\,\sin \,\left( {\frac{{2\pi }}{3}x} \right)\,\cos \,(120\,\pi t)$

where $x$ and $y$ are in $metre$ and $t$ in $second$ . The length of the string is $1.5\,m$ and its mass is $3.0\times 10^{-2}\,kg$ the tension in the string will be …. $N$

A stretched string is vibrating in its $5^{th}$ harmonic as shown. Consider a particle $1(figure)$. At an instant this particle is at mean positions and is moving towards its negative extreme. Which of the following set of particles, are in same phase with particle $1$

A string under a tension of $129.6\,\, N$ produces $10\,\, beats /sec$  when it is vibrated along with a tuning fork. When the tension is the string is increased to $160\,\, N,$ it sounds in unison with same tuning fork. calculate fundamental freq. of tuning fork …. $Hz$