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

Figure, shows a stationary wave between two fixed points $P$ and $Q$. Which point$(s)$ of $1, 2$ and $3$ are in phase with the point $X?$

The frequency of transverse vibrations in a stretched string is $200 Hz$. If the tension is increased four times and the length is reduced to one-fourth the original value, the frequency of vibration will be  .... $Hz$

A transverse harmonic wave on a string is described by $y = 3 \sin \,(36t + 0.018x + \frac{\pi}{4})$ where $x$ and $y$ are in $cm$ and $t$ in $s$. The least distance between  two sucessive crests in the wave is .... $m$

The length of a sonometer wire tuned to a frequency of $250 Hz$ is $0.60$ metre. The frequency of tuning fork with which the vibrating wire will be in tune when the length is made $0.40$ metre is .... $Hz$

A string fixed at both ends vibrates in three loops. The wave length is $10\, cm$ . The length of string is .... $cm$