A source of unknown frequency gives \(4\) beats/s when sounded with a source of known frequency of \(250~\text{Hz}\). The second harmonic of the source of unknown frequency gives five beats per second when sounded with a source of frequency of \(513~\text{Hz}\). The unknown frequency will be:

Two sources of sound placed close to each other, are emitting progressive waves given by,
\(y_1=4\sin 600\pi t\) and \(y_2=5\sin 608\pi t\).
${}_{}$An observer located near these two sources of sound will hear:

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

A tuning fork of frequency \(512\) Hz makes \(4\) beats/s with the vibrating string of a piano. The beat frequency decreases to \(2\) beats/s when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was:
1. \(510\) Hz
2. \(514\) Hz
3. \(516\) Hz
4. \(508\) Hz

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. \(6\)