$A$ metal rod of length $125 \ cm$ is clamped at its midpoint. If the speed of sound in the metal is $5000 \ ms^{-1}$,then the fundamental frequency of the longitudinal vibrations of the rod is (in $kHz$)

$A$ pipe open at both ends and a pipe closed at one end have the same length. The ratio of the frequencies of the air columns in their $p^{\text{th}}$ overtone respectively is

One insulated conductor from a household extension cord has a mass per unit length of $\mu$. $A$ section of this conductor is held under tension between two clamps. $A$ subsection is located in a magnetic field of magnitude $B$ directed perpendicular to the length of the cord. When the cord carries an $AC$ current of $i$ at a frequency of $f$,it vibrates in resonance in its simplest standing-wave vibration state. Determine the relationship that must be satisfied between the separation $d$ of the clamps and the tension $T$ in the cord.

The vibrations of four air columns under identical conditions are represented in the figure below. The ratio of frequencies $n_p: n_q: n_r: n_s$ will be

In a resonance tube experiment,when the tube is filled with water up to a height of $17.0 \, cm$ from the bottom,it resonates with a given tuning fork. When the water level is raised,the next resonance with the same tuning fork occurs at a height of $24.5 \, cm$. If the velocity of sound in air is $330 \, m/s$,the tuning fork frequency is $...... \, Hz$.

An open organ pipe having fundamental frequency $(n)$ is in unison with a vibrating string. If the tube is dipped in water so that $75 \%$ of the length of the tube is inside the water,then the ratio of the fundamental frequency of the air column of the dipped tube to that of the string will be (Neglect end corrections).