# 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 |
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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. $$204.8~\text{Hz}$$
Subtopic: Â Standing Waves |
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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 |
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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 |
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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. $$1:16$$
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. $$\frac{\pi^2}{9}~\text{m}$$
Subtopic: Â Wave Motion |
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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 |
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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. $$2f_0$$
Subtopic: Â Standing Waves |
Â 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 |
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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 |
Â 76%
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