A harmonic wave on a string is given as $=15$sin $/160$

where x and y are in cm and t in s$.$

$($a$)$ Find the amplitude, wavelength, angular wave number, angular frequency, period, speed, direction of propagation.

$($b$)$ Where are the crests of the wave at the time t $=0$ s$?$

$($c$)$ Where are the crests of the wave at the time t $=1/16$ s$?$

$($d$)$ Show that the point at x $=0$ moves in a SHM$.$

$($e$)$ What is the phase difference between the points at x $=0$ and x $=10$ cm$?$

$($f$)$ What is the transverse velocity of the point at x $=0$ at times t $=0$ s and time t $=1/16$ s$?$