A wire having a linear mass density $9.0 \times 10^{-4} \;{kg} / {m}$ is stretched between two rigid supports with a tension of $900\; {N}$. The wire resonates at a frequency of $500\;{Hz}$. The next higher frequency at which the same wire resonates is $550\; {Hz}$. The length of the wire is $…… {m}$

The frequency of transverse vibrations in a stretched string is $200 Hz$. If the tension is increased four times and the length is reduced to one-fourth the original value, the frequency of vibration will be  …. $Hz$

A hollow pipe of length $0.8 \mathrm{~m}$ is closed at one end. At its open end a $0.5 \mathrm{~m}$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50 \mathrm{~N}$ and the speed of sound is $320 \mathrm{~ms}^{-1}$, the mass of the string is

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

A tuning fork vibrating with a frequency of $512$ $\mathrm{Hz}$ is kept close to the open end of a tube filled with water. The water level in the tube is gradually lowered. When the water level is $17$ $\mathrm{cm}$ below the open end, maximum intensity of sound is heard. If the room temperature is $20^{°}$ $\mathrm{C}$, calculate :

$(a)$ speed of sound in air at room temperature

$(b)$ speed of sound in air at $0^{°}$ $\mathrm{C}$.

$(c)$ if the water in the tube is replaced with mercury, will there be any difference in your observations ?