If the equation of a transverse wave is $y = 5\sin 2\pi \left[ \frac{t}{0.04} - \frac{x}{40} \right]$,where distance is in $cm$ and time is in seconds,then the wavelength of the wave is .... $cm$.

For a travelling harmonic wave $y(x, t) = 2.0 \cos 2\pi(10 t - 0.0080 x + 0.35)$, where $x$ and $y$ are in $\text{cm}$ and $t$ in $\text{s}$. The phase difference between oscillatory motion of two points separated by a distance of $0.5 \text{ m}$ is: (in $\pi \text{ rad}$)

The equation of a transverse wave is given by $y = 10\sin \pi (0.01x - 2t)$ where $x$ and $y$ are in $cm$ and $t$ is in seconds. Its frequency is .... $sec^{-1}$.

$A$ pulse on a string is shown in the figure. $P$ is a particle of the string. State which of the following is incorrect.

$A$ plane progressive wave is given by $y = 2 \cos 2 \pi (330 t - x) \ m$. The frequency of the wave is: (in $Hz$)

One end of a long string of linear mass density $8.0 \times 10^{-3} \; kg \; m^{-1}$ is connected to an electrically driven tuning fork of frequency $256 \; Hz$. The other end passes over a pulley and is tied to a pan containing a mass of $90 \; kg$. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At $t=0$,the left end (fork end) of the string $x=0$ has zero transverse displacement $(y=0)$ and is moving along the positive $y$-direction. The amplitude of the wave is $5.0 \; cm$. Write down the transverse displacement $y$ as a function of $x$ and $t$ that describes the wave on the string.