If \(n_1\), \(n_2\)_, and \(n_3\) are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency \(n\) of the string is given by:
1. \( \frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}\)
2. \( \frac{1}{\sqrt{n}}=\frac{1}{\sqrt{n_1}}+\frac{1}{\sqrt{n_2}}+\frac{1}{\sqrt{n_3}}\)
3. \( \sqrt{n}=\sqrt{n_1}+\sqrt{n_2}+\sqrt{n_3}\)
4. \( n=n_1+n_2+n_3\)

The number of possible natural oscillations of the air column in a pipe closed at one end of length \(85\) cm whose frequencies lie below \(1250\) Hz are:(velocity of sound= $\mathrm{}$\(340~\text{m/s}\)) 
1. \(4\)
2. \(5\)
3. \(7\)
4. \(6\)

A speeding motorcyclist sees a traffic jam ahead of him. He slows down to 36 km/hour. He finds that traffic has eased and a car moving ahead of him at 18 km/hour is honking at a frequency of 1392 Hz. If the speed of sound is 343 m/s, the frequency of the honk as heard by him will be:

1. 1332 Hz

2. 1372 Hz

3. 1412 Hz

4. 1454 Hz

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:

A wave traveling in the +ve \(x\text-\)direction having maximum displacement along \(y\text-\)direction as \(1~\text{m}\), wavelength \(2\pi~\text{m}\) and frequency of \(\frac{1}{\pi}~\text{Hz}\), is represented by:
1. \(y=\sin (2 \pi x-2 \pi t)\)
2. \(y=\sin (10 \pi x-20 \pi t)\)
3. \(y=\sin (2 \pi x+2 \pi t)\)
4. \( y=\sin (x-2 t)\)

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:

A transverse wave is represented by y = Asin(ωt -kx). At what value of the wavelength is the wave velocity equal to the maximum particle velocity?

1. $\pi$A/2

2. $\pi$A

3. 2$\pi$A

4. A