Two wires, \(A\) and \(B,\) of a musical instrument 'Sitar' produce \(3\) beats per second. If the tension of \(B\) is raised, the number of beats becomes \(1\) beat per second. If the frequency of \(A\) is \(450~\text{Hz}\), then the original frequency of \(B\) will be:
1. \(447~\text{Hz}\)
2. \(453~\text{Hz}\)
3. \(449~\text{Hz}\)
4. \(451~\text{Hz}\)

The fundamental frequency of an open organ pipe is \(200\) Hz. When the half-length of the pipe is immersed in water, the fundamental frequency of the air column in the pipe will be:
1. \(100\) Hz
2. \(200\) Hz
3. \(400\) Hz
4. \(800\) Hz

A vibrating tuning fork of frequency 1000 Hz is placed near the open end of a long cylindrical tube. The tube has a side opening and is also fitted with a movable reflecting piston. As the piston is moved through x distance, the intensity of sound changes from a maximum to a minimum for an observer at the side opening. If the speed of sound is 350 meters per second, then x is-

1. 35 cm

2. 17.5 cm

3. 8.75 cm

4. 10 cm

A source of sound placed at the open end of a resonance column sends an acoustic wave of pressure amplitude ${\rho }_0$ inside the tube. If the atmospheric pressure is ${\rho }_A$ , then the ratio of maximum and minimum pressure at the closed end of the tube will be :

1. $\frac{({\rho }_A+{\rho }_0)}{({\rho }_A-{\rho }_0)}$

2. $\frac{({\rho }_A+2{\rho }_0)}{({\rho }_A-2{\rho }_0)}$

3. $\frac{{\rho }_A}{{\rho }_A}$

4. $\frac{\left({\rho }_A+\frac{1}{2}{\rho }_0\right)}{\left({\rho }_A-\frac{1}{2}{\rho }_0\right)}$

 In a guitar, two strings \(A\) and \(B\) made of same material are slightly out of tune and produce beats of frequency \(6~\text{Hz}\). When tension in \(B\) is slightly decreased, the beat frequency increases to \(7~\text{Hz}\).  If the frequency of \(A\) is \(530~\text{Hz}\), the original frequency of \(B\) will be:

A stone dropped from the top of a tower of height \(300\) m splashes into the water of a pond near the base of the tower. When is the splash heard at the top?
(Given that the speed of sound in air is \(340\) m/s and \(g=9.8\) m/s²)
1. \(7.7\)
2. \(8.7\)
3. \(6.7\)
4. \(7.8\)

A steel wire has a length of \(12.0\) m and a mass of \(2.10\) kg. What should be the tension in the wire so that the speed of a transverse wave on the wire equals the speed of sound in dry air, at \(20^{\circ}\text{C}\) (which is \(343\) m/s)?
1. \(4.3\times10^3\) N
2. \(3.2\times10^4\) N
3. \(2.06\times10^4\) N
4. \(1.2\times10^4\) N