A string is stretched between fixed points separated by \(75.0~\text{cm}.\) It is observed to have resonant frequencies of \(420~\text{Hz}\) and \(315~\text{Hz}\). There are no other resonant frequencies between these two. The lowest resonant frequency for these strings is:

1.	\(155~\text{Hz}\)	2.	\(205~\text{Hz}\)
3.	\(10.5~\text{Hz}\)	4.	\(105~\text{Hz}\)

If n₁, n₂ and n₃ are, 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. 1/n=1/n₁+1/n₂+1/n₃
 

2. 1/√n=1/√n₁+1/√n₂+1/√n₃

3. √n=√n₁+√n₂+√n₃

4. n=n₁+n₂+n₃

A speed motorcyclist sees a traffic jam ahead of him. He slows down to 36km/h. He finds that traffic has eased and a car moving in front of him at 18km/h is honking at a frequency of 1392Hz. If the speed of sound is 343m/s, the frequency of the honk as heard by him will be 
1. 1332Hz
2. 1372Hz
3. 1412Hz
4. 1454Hz 

A wave travelling in the positive x-direction having maximum displacement along y-direction as 1m, wavelength 2π m and frequency of 1/π Hz is represented by

1. y=sin(x-2t)
2. y=sin(2πx-2πt)
3. y=sin(10πx-20πt)
4. y=sin(2πx+2πt)

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

1. Open end will be anti-node

2. Odd harmonics of the fundamental frequency will be generated

3. All harmonics of the fundamental frequency will be generated

4. Pressure change will be maximum at both ends

A source of unknown frequency gives 4 beats/s when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second when sounded with a source of frequency 513 Hz. The unknown frequency is

1. 254 Hz

2. 246 Hz

3. 240 Hz

4. 260 Hz

When a string is divided into three segments of lengths \(l_1,~l_2\text{ and }l_3,\) the fundamental frequencies of these three segments are \(\nu_1,~\nu_2\text{ and }\nu_3\) respectively. The original fundamental frequency \((\nu)\) of the string is:
1. \(\sqrt{\nu}=\sqrt{\nu_1}+\sqrt{\nu_2}+\sqrt{\nu_3}\)
2. \(\nu=\nu_1+\nu_2+\nu_3\)
3. \(\dfrac{1}{\nu}=\dfrac{1}{\nu_1}+\dfrac{1}{\nu_2}+\dfrac{1}{\nu_3}\)
4. \(\dfrac{1}{\sqrt{\nu}}=\dfrac{1}{\sqrt{\nu_1}}+\dfrac{1}{\sqrt{\nu_2}}+\dfrac{1}{\sqrt{\nu_3}}\)

Two sources of sound placed close to each other, are emitting progressive waves given by

${\mathrm{y}}_1$=4 sin 600$\mathrm{\pi t}$ and ${\mathrm{y}}_2$=5 sin 608 $\mathrm{\pi t}$

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 waxing and waning

The equation of a simple harmonic wave is given by 

          $\mathrm{y}=3<mspace\; width="1em"></mspace>\sin \frac{\mathrm{\pi }}{2}(50\mathrm{t}-\mathrm{x})$

where x and y are in meters and t is in seconds. The ratio of maximum particle velocity to the wave velocity is

1. $2\mathrm{\pi }$

2. $\frac{3}{2}\mathrm{\pi }$

3. $3\mathrm{\pi }$

4. $\frac{2}{3}\mathrm{\pi }$