A pipe length of \(85~\text{cm}\) is closed from one end. Find the number of possible natural oscillations of the air column in the pipe whose frequencies lie below \(1250~\text{Hz}\). The velocity of sound in air is \(340~\text{m/s}\):
1. \(8\)
2. \(6\)
3. \(4\)
4. \(12\)

A uniform string of length \(20~\text{m}\) is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is: (take \(g = 10~\text{ms}^{-2}\))
1. \( 2 \pi \sqrt{2}~\text{s} \)
2. \(2 ~\text{s} \)
3. \( 2 \sqrt{2}~\text{s} \)
4. \(\sqrt{2} ~\text{s} \)

A pipe open at both ends has a fundamental frequency \(f\) in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now:
1. \( \frac{f}{2} \)
2. \( \frac{3 f}{4} \)
3. \( 2 f \)
4. \(f\)

A granite rod of \(60~\text{cm}\) length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is \(2.7\times 10^{3}~\text{kg/m}^3\) and it's Young's modulus is \(9.27\times 10^{10}~\text{Pa}\). What will be the fundamental frequency of the longitudinal vibrations?
1. \(5~\text{kHz}\)
2. \(2.5~\text{kHz}\)
3. \(10~\text{kHz}\)
4. \(7.5~\text{kHz}\)

A wire of length \(2L\) is formed by joining two wires, \(A\) and \(B,\) each of the same length but with different radii, \(r\) and \(2r,\) respectively, and made of the same material. The wire vibrates at a frequency such that the joint between the two wires forms a node. If the number of antinodes in wire \(A\) is \(p\) and in wire \(B\) is \(q,\) the ratio \(p:q\) is:

A string is clamped at both the ends and it is vibrating in its \(4^{th}\) harmonic. The equation of the stationary wave is \(Y=0.3\sin(0.157 x)\cos(200\pi t)\). The length of the string is: (All quantities are in SI units.)
1. \(40~\text{m}\)
2. \(80~\text{m}\)
3. \(20~\text{m}\)
4. \(60~\text{m}\)