A string $2.0\, m$ long and fixed at its end is driven by a $240\, Hz$ vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is

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 respectively

A pulse or a wave train travels along a stretched string and reaches the fixed end of the string. It will be reflected back with

A string of $7 \;m$ length has a mass of $0.035\,kg$. If tension in the string is $60.5\; N,$ then speed of a wave on the string is .... $m/s$

Four wires of identical length, diameters and of the same material are stretched on a sonometre wire. If the ratio of their tensions is $1 : 4 : 9 : 16$ then the ratio of their fundamental frequencies are

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 ?