The length and diameter of a metal wire used in a sonometer are both doubled. The fundamental frequency will change from $n$ to:

$A$ tuning fork gives $5$ beats per second with $40 \ cm$ length of a sonometer wire. If the length of the wire is shortened by $1 \ cm$,the number of beats is still the same. The frequency of the fork is (in $Hz$)

$A$ 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

$A$ $1 \, cm$ long string vibrates with a fundamental frequency of $256 \, Hz$. If the length is reduced to $\frac{1}{4} \, cm$ keeping the tension unaltered,the new fundamental frequency will be: (in $, Hz$)

$A$ sonometer wire is stretched by hanging a metal bob,the fundamental frequency of the wire is $n_1$. When the bob is completely immersed in water,the frequency of vibration of the wire becomes $n_2$. The relative density of the metal of the bob is

If ${n_1}, {n_2}, {n_3}, \dots$ are the frequencies of segments of a stretched string,the frequency $n$ of the string is given by