A string in musical instrument is $50 cm$ long and its fundamental frequency is $800 Hz.$ If a frequency of $1000 Hz$ is to be produced, then required length of string is ….. $cm$

Figure shows a snapshot for a travelling sine wave along a string. Four elemental portions $a, b, c$ and $d$ are indicated on the string. The elemental portion which has maximum potential energy is/are

A tuning fork vibrating with a frequency of $512$ $\mathrm{Hz}$ is kept close to the open end of a tube filled with water. The water level in the tube is gradually lowered. When the water level is $17$ $\mathrm{cm}$ below the open end, maximum intensity of sound is heard. If the room temperature is $20^{°}$ $\mathrm{C}$, calculate :

$(a)$ speed of sound in air at room temperature

$(b)$ speed of sound in air at $0^{°}$ $\mathrm{C}$.

$(c)$ if the water in the tube is replaced with mercury, will there be any difference in your observations ?

A $43\, m$ long rope of mass $5.0\, kg$ joins two rock climbers. One climber strikes the  rope and the second one feels the effect $1.4\, s$ later. What is the tension in the rope …. $N$ ?

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 $X?$