$A$ plane wave is described by the equation $y = 3 \cos \left( \frac{x}{4} - 10t - \frac{\pi}{2} \right)$. The maximum velocity of the particles of the medium due to this wave is

Write the equation for wave speed in terms of wavelength and frequency.

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 $\pi \text{ rad}$)

In a simple harmonic wave,the minimum distance between particles in the same phase always having the same speed is ..........

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.

$A$ sinusoidal wave of wavelength $7.5 \ cm$ travels a distance of $1.2 \ cm$ along the $x$-direction in $0.3 \ s$. The crest $P$ is at $x = 0$ at $t = 0 \ s$ and the maximum displacement of the wave is $2 \ cm$. Which equation correctly represents this wave?