If n₁, n_2, and n₃ 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=$340 m/s$) 

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

If we study the vibration of a pipe open at both ends, then which of the following statements is not true:

1. Odd harmonics of the fundamental frequency will be generated

2. All harmonics of the fundamental frequency will be generated

3. Pressure change will be maximum at both ends

4. The open end will be an antinode

A source of unknown frequency gives 4 beats/s when sounded with a source of known frequency of 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second when sounded with a source of frequency of 513 Hz. The unknown frequency will be:
1. 246 Hz
2. 240 Hz
3. 260 Hz
4. 254 Hz

A wave travelling in the +ve x-direction having maximum displacement along y-direction as 1 m, wavelength $2\pi m$ and frequency of $\frac{1}{\mathrm{\pi }}$ Hz, is represented by:

$1. y=\sin \left(2\pi x-2\pi t\right)$
2. y=sin10πx-20πt
3. y=sin2πx+2πt
4. y=sinx-2t

Two sources of sound placed close to each other, are emitting progressive waves given by,
 $y_1$=4sin600$\pi$t and $y_2$=5sin608$\pi$t
An observer located near these two sources of sound will hear:

1. 4 beats per second with intensity ratio 25:16 between waxing and waning

2. 8 beats per second with intensity ratio 25:16 between waxing and waning

3. 8 beats per second with intensity ratio 81:1 between waxing and waning

4. 4 beats per second with intensity ratio 81:1 between waxing and waning

Two waves are represented by the equations $y_1=a \sin (\omega t+kx+0.57) m$ and $y_2=a\cos (\omega t+kx) m$, where x is in metres and t in seconds. The phase difference between them is:
1. 1.25 rad
2. 1.57 rad
3. 0.57 rad
4. 1.0 rad

Sound waves travel at 350 m/s through warm air and at 3500 m/s through brass. The wavelength of a 700 Hz acoustic wave as it enters brass from warm air:

1.  increase by a factor of 20

2.  increase by a factor of 10

3.  decrease by a factor of 20

4.  decrease by a factor of 10

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