An observer on a sea-coast counts $45$ waves in one minute. If the wavelength of the waves is $7 \ m$,then the velocity of the waves will be (in $m/s$)

$A$ simple harmonic progressive wave is given by $Y = Y_0 \sin 2 \pi (nt - \frac{x}{\lambda})$. If the wave velocity is $(1/8)^{\text{th}}$ of the maximum particle velocity,then the wavelength is

$A$ travelling harmonic wave on a string is described by $y(x, t) = 7.5 \sin (0.0050 x + 12 t + \pi / 4)$.
$(a)$ What are the displacement and velocity of oscillation of a point at $x = 1 \; cm$ and $t = 1 \; s$? Is this velocity equal to the velocity of wave propagation?
$(b)$ Locate the points of the string which have the same transverse displacements and velocity as the $x = 1 \; cm$ point at $t = 2 \; s, 5 \; s$ and $11 \; s$.

The displacement of a wave is expressed as $x(t) = 5 \cos \left(628 t + \frac{\pi}{2}\right) \text{ m}$. The wavelength of the wave when its velocity is $300 \text{ m/s}$ is: (in $\text{ m}$)

$A$ longitudinal wave is represented by $x = 10 \sin 2 \pi (nt - \frac{x}{\lambda}) \, cm$. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to .....................

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