The fundamental frequency of a sonometer wire is $n$. If the tension is increased $3$ times,the length is increased $3$ times,and the diameter is increased $2$ times,what will be the new frequency?

$A$ string of length $2 \ m$ is fixed at both ends. If this string vibrates in its fourth normal mode with a frequency of $500 \ Hz$,then the waves would travel on it with a velocity of ..... $m/s$.

$A$ stretched wire of length $260 \ cm$ is set into vibrations. It is divided into three segments whose frequencies are in the ratio $2:3:4$. Their lengths must be

$A$ piano wire with a diameter of $0.90 \ mm$ is replaced by another wire of diameter $0.93 \ mm$ of the same material. If the tension of the wire is kept the same,then the percentage change in the frequency of the fundamental tone is

$A$ metal wire of linear mass density of $9.8 \, g/m$ is stretched with a tension of $10 \, kg$ weight between two rigid supports $1 \, m$ apart. The wire passes at its middle point between the poles of a permanent magnet,and it vibrates in resonance when carrying an alternating current of frequency $n$. The frequency $n$ of the alternating source is ..... $Hz$.

The frequency of the first harmonic of a string stretched between two points is $100 \, Hz$. The frequency of the third overtone is ... $Hz$.