A wave is travelling in the negative x direction having displacement 3 cm along Y direction, wavelength $2 \pi \mathrm{~m}$ and frequency $\left(\frac{1}{2 \pi}\right) \mathrm{Hz}$ is represented as ( $t=$ time)

A passenger is sitting in a train which is moving fast. The engine blows a whistle of frequency ' n '. If the apparent frequency of sound heard by the passenger is $n^1$ then

Two points on a travelling wave having frequency 500 Hz and velocity $300 \mathrm{~m} / \mathrm{s}$ are $30^{\circ}$ out of phase, then the minimum distance between the two points is

A simple harmonic progressive wave is given by $y=A \sin 2 \pi\left(n t-\frac{x}{\lambda}\right)$. If the wave velocity is equal to $=\frac{1}{3}$ (maximum particle velocity) then the wavelength $\lambda$ is given by