$A$ second harmonic has to be generated in a string of length $l$ stretched between two rigid supports. The points where the string has to be plucked and touched are

$A$ sonometer wire is vibrating in the third overtone. There are:

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.

$A$ guitar string of length $90\,cm$ vibrates with a fundamental frequency of $120\,Hz.$ The length of the string producing a fundamental frequency of $180\,Hz$ will be $...........cm$.

$A$ wire having a linear mass density $9.0 \times 10^{-4} \; \text{kg/m}$ is stretched between two rigid supports with a tension of $900 \; \text{N}$. The wire resonates at a frequency of $500 \; \text{Hz}$. The next higher frequency at which the same wire resonates is $550 \; \text{Hz}$. The length of the wire is $...... \; \text{m}$.

The tension in a wire is decreased by $19 \%$. The percentage decrease in frequency will be ......... $\%$