A string fixed at both ends resonates at a certain fundamental frequency. Which of the following adjustments would not affect the fundamental frequency?

A string on a musical instrument is $50 cm$ long and its fundamental frequency is $270 Hz$. If the desired frequency of $1000 Hz$ is to be produced, the required length of the string is …. $cm$

A vibrating string of certain length $l$ under a tension $T$ reasonates with a mode corresponding to the first overtone (third harmonic) of an air column of length $75$ $cm$ inside a tube closed at one end. The string also generates $4$ beats per second when excited along with a tuning fork of frequency $n$. Now when the tension of the string is slightly increased the number of beats reduces to $2$ per second. Assuming the velocity of sound in air to be $340$ $m/s$, the frequency $n$ of the tuning fork in $Hz $ is

The sound carried by air from a sitar to a listener is a wave of the following type

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