A vibrating string of certain length $l$ under a tension $T$ resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length $75\, cm$ inside a tube closed at one end. The string also generates $4\, beats$ per second when excited along with a tuning fork of frequency $n$. Now when the tension of the string is slightly increased the number of beats reduces to $2\, per second$. Assuming the velocity of sound in air to be $340\, m/s$, the frequency $n$ of the tuning fork in $Hz$ is

The transverse displacement of a string (clamped at its both ends) is given by

$y(x,t)\, = \,0.6\,\sin \,\left( {\frac{{2\pi }}{3}x} \right)\,\cos \,(120\,\pi t)$

where $x$ and $y$ are in $metre$ and $t$ in $second$ . The length of the string is $1.5\,m$ and its mass is $3.0\times 10^{-2}\,kg$ the tension in the string will be …. $N$

A tuning fork vibrating with a sonometer having $20 cm$ wire produces $5$ beats per second. The beat frequency does not change if the length of the wire is changed to $21 cm.$ the frequency of the tuning fork (in Hertz) must be

For a transverse wave travelling along a straight line, the distance between two peaks (crests) is $5 \,m ,$ while the distance between one crest and one trough is $1.5 \,m$ The possible wavelengths (in $m$ ) of the waves are

A string is clamed at both the ends and it is vibrating in its $4^{th}$ harmonic. The equation of the stationary wave is $Y =0.3\,sin\,(0.157\,x) \,cos\,(200\pi t)$. The length of the string is ….. $m$ (all quantities are in $SI$ units)