$A$ transverse wave given by $y=2 \sin (0.01 x+30 t)$ moves on a stretched string from one end to another end in $0.5 \ s$. If $x$ and $y$ are in $cm$ and $t$ is in $s$,then the length of the string is: (in $m$)

The distance between two consecutive points with a phase difference of $60^{\circ}$ in a wave of frequency $500 \text{ Hz}$ is $0.6 \text{ m}$. The velocity with which the wave is travelling is: (in $\text{ km/s}$)

$A$ plane progressive wave is given by $y = 2 \cos 6.284(330t - x)$. What is the period of the wave?

Write the equation of displacement of an element of a medium in a harmonic wave.

$A$ body sends a wave $150 \text{ mm}$ long through medium $P$ and $0.30 \text{ m}$ long in medium $Q$. If velocity of the wave in medium $P$ is $80 \text{ cm s}^{-1}$, the velocity of wave in medium $Q$ is (in $\text{ m s}^{-1}$)

$A$ transverse sinusoidal wave of amplitude '$a$',wavelength $\lambda$,and frequency $f$ is travelling on a stretched string. The maximum speed at any point on the string is $v/10$,where $v$ is the speed of propagation of the wave. If $a = 10^{-3} \ m$ and $v = 10 \ ms^{-1}$,then $\lambda$ and $f$ are given by: