Q. No.A standing wave is formed by the superposition of two waves traveling in opposite directions. The transverse displacement is given by \(y(x,t)=0.5\sin\left(\frac{5\pi}{4}x\right) \cos(200\pi t).\) What is the speed of the traveling wave moving in the positive \(x\) direction?
\((x\) and \(t\) are in meters and seconds, respectively.)
1. \(180~\text{m/s}\)
2. \(160~\text{m/s}\)
3. \(120~\text{m/s}\)
4. \(90~\text{m/s}\)
\((x\) and \(t\) are in meters and seconds, respectively.)
1. \(180~\text{m/s}\)
2. \(160~\text{m/s}\)
3. \(120~\text{m/s}\)
4. \(90~\text{m/s}\)
Subtopic: Â Standing Waves |
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A pipe of length \(11~\text{cm}\) is closed at one end. The first harmonic frequency of the pipe in the air at \(0^\circ \text{C}\) is:
(the velocity of sound at \(0^\circ \text{C}=330~\text{m/s}\))
1. \(1200~\text{Hz}\)
2. \(1000~\text{Hz}\)
3. \(800~\text{Hz}\)
4. \(750~\text{Hz}\)
(the velocity of sound at \(0^\circ \text{C}=330~\text{m/s}\))
1. \(1200~\text{Hz}\)
2. \(1000~\text{Hz}\)
3. \(800~\text{Hz}\)
4. \(750~\text{Hz}\)
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A string is fixed at both ends and set to vibrate in five loops. If the wavelength is \(8\) cm then the length of the string is:
1. \(10 \) cm
2. \(15\) cm
3. \(20\) cm
4. \(25\) cm
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If the speed of sound in air is \(v,\) then the minimum possible length of the closed-end organ pipe which resonates to frequency \(f\) will be:
| 1. | \(\dfrac{v}{2f}\) | 2. | \(\dfrac{v}{4f}\) |
| 3. | \(\dfrac{v}{3f}\) | 4. | \(\dfrac{v}{f}\) |
Subtopic: Â Standing Waves |
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Two waves executing simple harmonic motion travelling in the same direction with the same amplitude and frequency are superimposed. The resultant amplitude is equal to the \(\sqrt 3 \) times of amplitude of individual motions. The phase difference between the two motions is:
| 1. | \(30^{\circ}\) | 2. | \(45^{\circ}\) |
| 3. | \(60^{\circ}\) | 4. | \(90^{\circ}\) |
Subtopic: Â Standing Waves |
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When a string is divided into three segments of lengths \(l_1\), \(l_2\) and \(l_3\), the fundamental frequencies of these three segments are \(\nu_1\), \(\nu_2\) 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. | \(\dfrac{1}{\sqrt{\nu}} =\dfrac{1}{\sqrt{\nu_1}} +\dfrac{1}{\sqrt{\nu_2}}+\dfrac{1}{\sqrt{\nu_3}}\) |
Subtopic: Â Standing Waves |
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AIPMT - 2012
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A string, under tension, and lying along the \(x\)-axis is set into transverse vibrations. The displacement at a point \(x\) is given by the function \(y(x,t)\) where \(t\) represents the time: \(y(x,t)=\left ( 3~\text{mm} \right )\mathrm{sin}\left ( \frac{\pi x}{20~\text{cm}} \right ) \)\(\mathrm{cos}\left\{2\pi\left ( 100~\text{s}^{-1} \right )t \right\}\)
The maximum amplitude of vibration at any point on the string is:
1. \(3~\text{mm}\)
2. \(20~\text{cm}\)
3. \(300~\text{mm}\)
4. \(15~\text{mm}\)
The maximum amplitude of vibration at any point on the string is:
1. \(3~\text{mm}\)
2. \(20~\text{cm}\)
3. \(300~\text{mm}\)
4. \(15~\text{mm}\)
Subtopic: Â Standing Waves |
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A pipe is \(15\) cm long and is open at both ends. Which harmonic mode of the pipe will resonate with a \(2.2\) kHz sound source?
(Given: the velocity of sound in air \(=330\) m/s)
| 1. | fundamental | 2. | second harmonic |
| 3. | third harmonic | 4. | fourth harmonic |
Subtopic: Â Standing Waves |
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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 this string is:
| 1. | \( 155~\text{Hz} \) | 2. | \( 205~\text{Hz} \) |
| 3. | \( 10.5~\text{Hz} \) | 4. | \( 105~\text{Hz} \) |
Subtopic: Â Standing Waves |
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NEET - 2015
Hints
Which of the following statements are true for a stationary wave?
Choose the correct option:
1. (a), (c)
2. (a), (b), (d), (e)
3. (b), (d)
4. (c), (d)
| (a) | Every particle has a fixed amplitude which is different from the amplitude of its nearest particle. |
| (b) | All the particles cross their mean position at the same time. |
| (c) | All the particles are oscillating with same amplitude. |
| (d) | There is no net transfer of energy across any plane. |
| (e) | There are some particles which are always at rest. |
1. (a), (c)
2. (a), (b), (d), (e)
3. (b), (d)
4. (c), (d)
Subtopic: Â Standing Waves |
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