The velocity of waves in a string fixed at both ends is $2 m/s$. The string forms standing waves with nodes $5.0 cm$ apart. The frequency of vibration of the string in $Hz$ is

A string of length $1\, m$ and mass $5\, g$ is fixed at both ends. The tension in the string is $8.0\, N$. The string is set into vibration using an external vibrator of frequency $100\, Hz$. The separation between successive nodes on the string is close to …. $cm$

A string is producing transverse vibration whose equation is $y = 0.021\;\sin (x + 30t)$, Where $x$ and $y$ are in meters and $t$ is in seconds. If the linear density of the string is $1.3 \times {10^{ – 4}}\,kg/m,$ then the tension in the string in $N$ will be

The equation of stationary wave along a stretched string is given by $y = 5\sin \frac{{\pi x}}{3}\cos 40\pi t$ where $x$ and $y$ are in centimetre and $t$ in second. The separation between two adjacent nodes is …. $cm$

A sonometer wire of length $114\, cm$ is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio $1 : 3 : 4$ ?