At the poles of the earth,a stretched wire of a given length vibrates in unison with a tuning fork. At the equator of the earth,for the same setting,to produce resonance with the same fork,the vibrating length of the wire

$A$ uniform wire of length $L$,diameter $D$,and density $\rho$ is stretched by a tension $T$. The frequency $f$ of the wire is proportional to:

$A$ sonometer wire resonates with $4$ antinodes between the two bridges for a given tuning fork when a $1 \text{ kg}$ mass is suspended from the wire. Using the same fork, when mass $M$ is suspended, the wire resonates producing $2$ antinodes between the two bridges. (The distance between the bridges remains the same). The value of $M$ is: (in $\text{ kg}$)

Unlike a laboratory sonometer,a stringed instrument is seldom plucked in the middle. Supposing a sitar string is plucked at about $\frac{1}{4}$th of its length from the end. The most prominent harmonic would be

$A$ stationary wave is produced along a stretched string of length $80 \,cm$. The resonant frequencies of the string are $90 \,Hz$, $150 \,Hz$, and $210 \,Hz$. The speed of the transverse wave in the string is: (in $\,m/s$)

Length of a sonometer wire is either $95 \ cm$ or $100 \ cm$. In both the cases,a tuning fork produces $5 \ beats/sec$ with the wire. The frequency of the tuning fork is- (in $Hz$)