$A$ longitudinal wave is represented by $x=x_0 \sin 2 \pi(n t-x / \lambda)$. The maximum particle velocity will be four times the wave velocity if:

The number of waves contained in unit length of the medium is called

The equation of a sound wave is $y = 0.0015 \sin (62.4x + 316t)$. The wavelength of this wave is ..... $unit$.

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

State whether the following statements are True or False:
$(i)$ In the case of propagation of longitudinal waves,the angle between the directions of particle velocity and wave velocity is $0^{\circ}$ or $180^{\circ}$.
$(ii)$ In the case of propagation of transverse waves,the angle between the directions of particle velocity and wave velocity is $\pi \text{ rad}$.
$(iii)$ Along the direction of propagation of a wave,the distance between two particles having the same phase is called the wavelength of the wave.
$(iv)$ When a wave is reflected from a rarer medium,its phase increases by an amount of $\pi \text{ rad}$.

$A$ transverse progressive wave on a stretched string has a velocity of $10\,m/s$ and a frequency of $100\,Hz$. The phase difference between two particles of the string which are $2.5\,cm$ apart will be: