Q. No.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 \(10\).
Which one of the following statements is true?
| 1. | Both light and sound waves in the air are transverse. |
| 2. | The sound waves in the air are longitudinal while the light waves are transverse. |
| 3. | Both light and sound waves in the air are longitudinal. |
| 4. | Both light and sound waves can travel in a vacuum. |
Wave \(1\): \(y(x,t)= (2~\text{cm})\sin(3x-6t)\)
Wave \(2\): \(y(x,t)= (3~\text{cm})\sin(4x-12t)\)
Wave \(3\): \(y(x,t)= (4~\text{cm})\sin(5x-11t)\)
where \(x\) is in meters and \(t\) is in seconds. Of these waves:
| 1. | Wave \(1\) has the highest wave speed as well as the maximum transverse string speed. |
| 2. | Wave \(2\) has the highest wave speed, while Wave \(1\) has the maximum transverse string speed. |
| 3. | Wave \(3\) has the highest wave speed as well as the maximum transverse string speed. |
| 4. | Wave \(2\) has the highest wave speed, while Wave \(3\) has the maximum transverse string speed. |
A string of length \(3\) m and a linear mass density of \(0.0025\) kg/m is fixed at both ends. One of its resonance frequencies is \(252\) Hz. The next higher resonance frequency is \(336\) Hz. Then the fundamental frequency will be:
1. \(84~\text{Hz}\)
2. \(63~\text{Hz}\)
3. \(126~\text{Hz}\)
4. \(168~\text{Hz}\)
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:
| 1. | \(246~\text{Hz}\) | 2. | \(240~\text{Hz}\) |
| 3. | \(260~\text{Hz}\) | 4. | \(254~\text{Hz}\) |
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 |
A uniform rope, of length \(L\) and mass \(m_1\), hangs vertically from a rigid support. A block of mass \(m_2\) is attached to the free end of the rope. A transverse pulse of wavelength \(\lambda_1\) is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is \(\lambda_2\). The ratio \(\frac{\lambda_2}{\lambda_1}\) is:
1. \(\sqrt{\frac{m_1+m_2}{m_2}}\)
2. \(\sqrt{\frac{m_2}{m_1}}\)
3. \(\sqrt{\frac{m_1+m_2}{m_1}}\)
4. \(\sqrt{\frac{m_1}{m_2}}\)
| 1. | \(100~\text{cm}\) | 2. | \(150~\text{cm}\) |
| 3. | \(200~\text{cm}\) | 4. | \(66.7~\text{cm}\) |
The speed of sound in a medium is \(v\). If the density of the medium is doubled at constant pressure, what will be the new speed of sound?
| 1. | \(\sqrt{2} v \) | 2. | \(v \) |
| 3. | \(\frac{v}{\sqrt{2}} \) | 4. | \(2v\) |
1. \(\alpha = 25.00\pi, \beta = \pi\)
2. \(\alpha = \frac{0.08}{\pi}, \beta = \frac{2.0}{\pi}\)
3. \(\alpha = \frac{0.04}{\pi}, \beta = \frac{1.0}{\pi}\)
4. \(\alpha = 12.50\pi, \beta = \frac{\pi}{2.0}\)
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