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

$A$ string 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 ..... $m/s$.

$A$ string of length $1\, m$ and mass $5\, g$ is fixed at both ends. The tension in the string is $8.0\, N$. The string is set into vibration using an external vibrator of frequency $100\, Hz$. The separation between successive nodes on the string is close to .... $cm$

$A$ 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 string of a violin has a frequency of $440 \,cps$. If the violin string is shortened by one fifth,its frequency will be changed to ........... $cps$.

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