In a resonance tube,two successive positions of resonance are obtained at $15 \, cm$ and $48 \, cm$. If the frequency of the tuning fork is $500 \, Hz$,the velocity of sound is ......... $m/s$.

$A$ person blows into the open end of a long pipe. As a result,a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe,which of the following statements are true?
$(I)$ $A$ high-pressure pulse starts travelling up the pipe,if the other end of the pipe is open.
$(II)$ $A$ low-pressure pulse starts travelling up the pipe,if the other end of the pipe is open.
$(III)$ $A$ low-pressure pulse starts travelling up the pipe,if the other end of the pipe is closed.
$(IV)$ $A$ high-pressure pulse starts travelling up the pipe,if the other end of the pipe is closed.

Tube $A$ has both ends open while tube $B$ has one end closed,otherwise they are identical. The ratio of the fundamental frequency of tube $A$ to tube $B$ is

$A$ tuning fork of frequency $500 \ Hz$ is sounded on a resonance tube. The first and second resonance are obtained at $17 \ cm$ and $52 \ cm$. The velocity of sound is $........ \ m/s$.

Two closed pipes have the same fundamental frequency. One is filled with oxygen and the other with hydrogen at the same temperature. The ratio of their lengths 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.