Sound Waves

$$\begin{array} { l } { \text { A pipe of length } 2 \mathrm { m } \text { is open at both ends. The speed of sound in air is } 340 \mathrm { m } / \mathrm { s } . \text { The air column } } \\ { \text { can resonate in frequency: } } \end{array}$$
One end of a long string of linear mass density 8.0 $$\times \displaystyle 10^{-3}  $$ kg $$ \displaystyle m^{-1}  $$ is connected to an electrically driven tuning fork of frequency 256 Hz. The other end passes over a pulley and is tied to a pan containing a mass of 90 kg. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At t = 0, the left end (fork end) of the string x = 0 has zero transverse displacement (y = 0) and is moving along positive y-direction. The amplitude of the wave is 5.0 cm. Write down the transverse displacement y as function of x and t that describes the wave on the string :
The figure shows variation of displacement of particles in a closed organ pipe for $$3^{rd}$$ overtone. What is Amplitude at P. Diameter of pipe =2 m :

The frequency of fork is 512 Hz and the sound produced by it travels 42 metres as the tuning fork completes 64 vibrations. Find the velocity of sound :
The wavelength of waves produced on the surface of water is 20 cm. If the wave velocity is 24 m $$s^{-1}$$, calculate the time in which one wave is produced ?