A transverse wave is described by the equation $y = {y_0}\,\sin \,2\pi \left( {ft – \frac{x}{\lambda }} \right)$ . The maximum particle velocity is equal to four times the wave velocity if

Equation of a plane progressive wave is given by $y = 0.6\sin 2\pi \left( {t – \frac{x}{2}} \right)$. On reflection from a denser medium its amplitude becomes $2/3$ of the amplitude of the incident wave. The equation of the reflected wave is

The figure represents the instantaneous picture of a transverse harmonic wave traveling along the negative $x$-axis. Choose the correct alternative $(s)$ related to the movement of the nine points shown in the figure.  The stationary points is/are

A car $P$ approaching a crossing at a speed of $10\, m/s$ sounds a horn of frequency $700\, Hz$ when $40\, m$ in front of the crossing. Speed of sound in air is $340\, m/s$. Another car $Q$ is at rest on a road which is perpendicular to the road on which car $P$ is reaching the crossing (see figure). The driver of car $Q$ hears the sound of the horn of car $P$ when he is $30\, m$ in front of the crossing. The apparent frequency heard by the driver of car $Q$ is   …. $Hz$

A string of mass $M$ and length $L$ hangs freely from a fixed point. The velocity of transverse wave along the string at a distance $'x'$ from the free end will be