A progressive wave travelling along the positive $x-$ direction is represented by $y\left(x,\mathrm{t}\right)=\mathrm{A}\mathrm{ }\mathrm{s}\mathrm{i}\mathrm{n}(\mathrm{k}x-\mathrm{\omega }\mathrm{t}+\mathrm{\varphi })$ . Its snapshot at $\mathrm{t}=0$ is given in the figure.

For this wave, the phase $\mathrm{\varphi }$ is:

A source of sound is at one end of a hollow tube. An observer at another end hears two distinct notes after a time interval of $1$ $ \mathrm{s}$. If velocity of sound in air is $340$ $ \mathrm{m}$ $ \mathrm{s}^{-1}$ and in metal is $3740$ $ \mathrm{m}$ $ \mathrm{s}^{-1}$, then the length of pipe is,

In a long cylindrical tube, the water level is adjusted and the air column is made to vibrate in unison with a vibrating tuning fork kept at the open end. Resonances are obtained when lengths of air column are

Air is blown at the mouth of an open tube of length $25$ $ \mathrm{cm}$ and diameter $2$ $ \mathrm{cm}$. If the velocity of sound in air is $330$ $ \mathrm{m}$ $\mathrm{s}^{-1}$, then emitted frequencies are (in $\mathrm{Hz}$),

What is the minimum length of a tube open at both ends that resonates with tuning fork of frequency $350$ $\mathrm{Hz}$? [velocity of sound in air $=$ $350$ $ \mathrm{m}$ $ \mathrm{s}^{-1}]$

In a pipe open at both ends, $n_{1}$ and $n_{2}$ are the frequencies corresponding to vibrating lengths $l_{1}$ and $l_{2}$, respectively. The end correction is,