The equation of a standing wave in a string fixed at both ends is given as $y=2 A \sin k x \cos \omega t$ The amplitude and frequency of a particle vibrating at the mid of an antinode and a node are respectively
$A, \frac{\omega}{2 \pi}$
$\frac{A}{\sqrt{2}}, \frac{\omega}{2 \pi}$
$A, \frac{\omega}{\pi}$
$\sqrt{2} A, \frac{\omega}{2 \pi}$
A wave is reflected from a rigid support. The change in phase on reflection will be
The tension in a wire is decreased by $19 \%$. The percentage decrease in frequency will be ......... $\%$
A string of length $1\,\,m$ and linear mass density $0.01\,\,kgm^{-1}$ is stretched to a tension of $100\,\,N.$ When both ends of the string are fixed, the three lowest frequencies for standing wave are $f_1, f_2$ and $f_3$. When only one end of the string is fixed, the three lowest frequencies for standing wave are $n_1, n_2$ and $n_3$. Then
A standing wave exists in a string of length $150\ cm$ , which is fixed at both ends with rigid supports . The displacement amplitude of a point at a distance of $10\ cm$ from one of the ends is $5\sqrt 3\ mm$ . The nearest distance between the two points, within the same loop and havin displacment amplitude equal to $5\sqrt 3\ mm$ is $10\ cm$ . Find the maximum displacement amplitude of the particles in the string .... $mm$
A sine wave of wavelength $\lambda $ is travelling in a medium. The minimum distance between the two particles, always having same speed, is