The length of a wire between the two ends of a sonometer is \(100\) cm. What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio \(1:3:5\)?
1. \(\frac{1500}{23} \mathrm{~cm}, \frac{500}{23} \mathrm{~cm} \)
2. \(\frac{1500}{23} \mathrm{~cm}, \frac{300}{23} \mathrm{~cm} \)
3. \(\frac{300}{23} \mathrm{~cm}, \frac{1500}{23} \mathrm{~cm} \)
4. \(\frac{1500}{23} \mathrm{~cm}, \frac{2000}{23} \mathrm{~cm}\)

Two identical piano wires, kept under the same tension T, have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to the occurrence of 6 beats/s when both the wires oscillate together would be:

1. 0.01

2. 0.02

3. 0.03

4. 0.04

The equation of a simple harmonic wave is given by \(y=3\sin \frac{\pi}{2}(50t-x)\) where \(x \) and \(y\) are in meters and \(t\) is in seconds. The ratio of maximum particle velocity to the wave velocity is:

Which one of the following statements is true?

The time of reverberation of a room \(A\) is one second. What will be the time (in seconds) of reverberation of a room, having all the dimensions double those of room A?

1. 2

2. 4

3. $\frac{1}{2}$

4. 1

A transverse wave propagating along the \(x\text-\)axis is represented by:
\(y(x,t)=8.0\sin\left(0.5\pi x-4\pi t-\frac{\pi}{4}\right)\), where \(x\) is in meters and \(t\) in seconds. The speed of the wave is: 
1. \(4\pi\) m/s
2. \(0.5\) m/s
3. \(\frac{\pi}{4}\) m/s
4. \(8\) m/s

Two sound waves with wavelengths \(5.0~\text{m}\) and \(5.5~\text{m}\), respectively, propagate in gas with a velocity of \(330~\text{m/s}\). How many beats per second can we expect?
1. \(12\)
2. \(0\)
3. \(1\)
4. \(6\)

The wave described by \(y=0.25\sin (10\pi x-2\pi t)\), where \(x \) and \(y\) are in metre and \(t\) in second, is a wave travelling along the: