$A$ transverse wave is represented by $y = \frac{10}{\pi} \sin \left( \frac{2\pi}{T}t - \frac{2\pi}{\lambda}x \right)$. For what value of the wavelength is the wave velocity twice the maximum particle velocity (in $cm$)?

Two waves are represented by the equations $y_1 = a \sin \omega t$ and $y_2 = a \cos \omega t$. The first wave

$A$ wave equation is $y = 10^{-4} \sin(60t + 2x)$,where $x$ and $y$ are in $m$ and $t$ is in $s$. Which of the following statements is correct?

Give the definition,equation,and unit for wavelength and wave number for a wave.

In a transverse wave,the distance between a crest and the neighbouring trough at the same instant is $4.0 \, cm$,and the distance between a crest and trough at the same place is $1.0 \, cm$. The next crest appears at the same place after a time interval of $0.4 \, s$. The maximum speed of the vibrating particles in the medium is

$A$ transverse wave is represented by the equation $y=2 \sin (30 t-40 x)$ where the measurements of distances are in meters,then the velocity of propagation is (in $ms^{-1}$)