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 ?

A string is rigidly tied at two ends and its equation of vibration is given by $y = \cos 2\pi \,t\sin \sin \pi x.$ Then minimum length of string is …. $m$

If the length of stretched string is shortened by $40\%$ and the tension is increased by $44\%$, then the ratio of the final and initial fundamental frequencies is

A stretched string is vibrating in its $5^{th}$ harmonic as shown. Consider a particle $1(figure)$. At an instant this particle is at mean positions and is moving towards its negative extreme. Which of the following set of particles, are in same phase with particle $1$

A tuning fork of frequency $480 Hz$ produces $10$ beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string if a slight increase in tension produces lesser beats per second than before ….. $Hz$