A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is:

1. 155 Hz

2. 205 Hz

3. 10.5 Hz

4. 105 Hz

The fundamental frequency of a closed organ pipe of a length 20 cm is equal to the second overtone of an organ pipe open at both ends. The length of the organ pipe open at both ends will be:
1. 80 cm
2. 100 cm
3. 120 cm
4. 140 cm
 

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