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Q. No.The equation \(y(x,t) = 0.005 \cos (\alpha x- \beta t)\) describes a wave traveling along the \(x\text-\)axis. If the wavelength and the time period of the wave are \(0.08~\text{m}\) and \(2.0~\text{s}\), respectively, then \(\alpha\) and \(\beta\) in appropriate units are:
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. \(\alpha = 12.50\pi, \beta = \frac{\pi}{2.0}\)
Subtopic: Â Wave Motion |
 87%
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In an experiment with a sonometer, a tuning fork of frequency \(256~\text{Hz}\) resonates with a length of \(25~\text{cm}\) and another tuning fork resonates with a length of \(16~\text{cm}\). If the tension of the string remains constant, then the frequency of the second tuning fork will be:
1. \(163.84~\text{Hz}\)
2. \(400~\text{Hz}\)
3. \(320~\text{Hz}\)
4. \(204.8~\text{Hz}\)
1. \(163.84~\text{Hz}\)
2. \(400~\text{Hz}\)
3. \(320~\text{Hz}\)
4. \(204.8~\text{Hz}\)
Subtopic: Â Standing Waves |
 75%
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The rate of energy transfer in a wave depends:
| 1. | directly on the square of the wave amplitude and square of the wave frequency. |
| 2. | directly on the square of the wave amplitude and square root of the wave frequency. |
| 3. | directly on the wave frequency and square of the wave amplitude. |
| 4. | directly on the wave amplitude and square of the wave frequency. |
Subtopic: Â Energy of Waves |
 72%
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A tuning fork with a frequency of \(800\) Hz produces resonance in a resonance column tube with the upper end open and the lower end closed by the water surface. Successive resonances are observed at lengths of \(9.75\) cm, \(31.25\) cm, and \(52.75\) cm. The speed of the sound in the air is:
| 1. | \(500\) m/s | 2. | \(156\) m/s |
| 3. | \(344\) m/s | 4. | \(172\) m/s |
Subtopic: Â Speed of Sound |
 74%
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NEET - 2019
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Two waves represented by the following equations are travelling in the same medium \(y_1 = 5 \sin2\pi (75t-0.25x)\), \(y_2 = 10 \sin2\pi (150t-0.50x)\). The intensity ratio \(\frac{I_1}{I_2}\) of the two waves will be:
1. \(1:2\)
2. \(1:4\)
3. \(1:8\)
4. \(1:16\)
1. \(1:2\)
2. \(1:4\)
3. \(1:8\)
4. \(1:16\)
Subtopic: Â Energy of Waves |
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Two progressive waves are represented by, \(y_1=5\sin(200t-3.14x)\) and
\(y_2=10\sin\left(200t-3.14x+\frac{\pi}{3}\right)\) (\(x\) is in metres, and \(t\) is in seconds). Path difference between the two waves is:
1. \(\frac{100}{\pi}~\text{m}\)
2. \(\frac{1}{3}~\text{m}\)
3. \(3.14\times \frac{\pi}{3}~\text{m}\)
4. \(\frac{\pi^2}{9}~\text{m}\)
\(y_2=10\sin\left(200t-3.14x+\frac{\pi}{3}\right)\) (\(x\) is in metres, and \(t\) is in seconds). Path difference between the two waves is:
1. \(\frac{100}{\pi}~\text{m}\)
2. \(\frac{1}{3}~\text{m}\)
3. \(3.14\times \frac{\pi}{3}~\text{m}\)
4. \(\frac{\pi^2}{9}~\text{m}\)
Subtopic: Â Wave Motion |
 72%
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If a travelling wave pulse is given by \(y=\frac{20}{4+(x+4 t)^2}~\text{m}\), then:
| 1. | the pulse is traveling along the negative \(x\text-\)axis. |
| 2. | the speed of the pulse is \(4\) m/s. |
| 3. | the amplitude of the pulse is \(5\) m. |
| 4. | all of these. |
Subtopic: Â Wave Motion |
 85%
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A cylindrical tube open at both ends has a fundamental frequency \(f_0\) in the air. The tube is dipped vertically in water such that half its length is inside water. The fundamental frequency of the air column now will be:
1. \(\frac{3f_0}{4}\)
2. \(f_0\)
3. \(\frac{f_0}{2}\)
4. \(2f_0\)
1. \(\frac{3f_0}{4}\)
2. \(f_0\)
3. \(\frac{f_0}{2}\)
4. \(2f_0\)
Subtopic: Â Standing Waves |
 68%
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The equation of a stationary wave is given as \(y =A\sin(0.5\pi t)\cos(0.2\pi x)\) where \(t\) is in seconds and \(x\) in centimetres. Which of the following is correct?
| 1. | Wavelength of the component waves is \(10~\text{cm}.\) |
| 2. | The separation between a node and the nearest antinode is \(2.5~\text{cm}.\) |
| 3. | Frequency of the component wave is \(0.25~\text{Hz}\). |
| 4. | All of these |
Subtopic: Â Standing Waves |
 89%
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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. \(168~\text{Hz}\)
Subtopic: Â Standing Waves |
 76%
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