A travelling wave $y=A\sin (kx-\omega t+\theta )$ passes from a heavier string to a lighter string. The reflected wave has amplitude $0.5 A$. The junction of the strings is at $x=0$. The equation of the reflected wave is

If vibrations of a string are to be increased by a factor of two, then tension in the string must be made 

The fundamental frequency of a string stretched with a weight of $4 \mathrm{kg}$ is $256 \mathrm{Hz}$. The weight required to produce its octave is 

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,

A source and an observer are situated on two perpendicular tracks as shown in the figure. The observer is at rest and the source is moving with a speed of $50 \mathrm{m} {\mathrm{s}}^{-1}$. The source emits a sound wave of frequency $75 \mathrm{Hz}$ which travel in the medium with a velocity of $200 \mathrm{m} {\mathrm{s}}^{-1}$. The frequency (in $\mathrm{Hz}$) of the sound heard by the observer when the source crosses the origin is,