Two identical strings $X$ and $Z$ made of the same material have tensions $T_{x}$ and $T_{z}$ in them. If their fundamental frequencies are $450\, Hz$ and $300\, Hz$,respectively,then the ratio $T_{x} / T_{z}$ 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

$A$ string fixed at both ends is vibrating in two segments. The wavelength of the corresponding wave is

The fundamental frequency of a sonometer wire increases by $6 \ Hz$ if its tension is increased by $44\%$ keeping the length constant. The change in the fundamental frequency of the sonometer wire in $Hz$ when the length of the wire is increased by $20\%$,keeping the original tension in the wire will be :-

$A$ tuning fork resonates with a sonometer wire of length $1 \ m$ stretched with a tension of $6 \ N$. When the tension in the wire is changed to $54 \ N$,the same tuning fork produces $12$ beats per second with it. The frequency of the tuning fork is $Hz$.

$A$ string vibrates with a frequency of $200 \ Hz$. When its length is doubled and tension is altered,it begins to vibrate with a frequency of $300 \ Hz$. The ratio of the new tension to the original tension is