# The equation $$y(x,t) = 0.005 ~cos (\alpha x- \beta t)$$ describes a wave traveling along the x-axis. If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then $\mathrm{\alpha }$ and $\mathrm{\beta }$ in appropriate units are: 1. $\mathrm{\alpha }=25.00$ $\mathrm{\pi },$ $\mathrm{\beta }=\mathrm{\pi }$ 2. $\mathrm{\alpha }=\frac{0.08}{\mathrm{\pi }},$ $\mathrm{\beta }=\frac{2.0}{\mathrm{\pi }}$ 3. $\mathrm{\alpha }=\frac{0.04}{\mathrm{\pi }},$ $\mathrm{\beta }=\frac{1.0}{\mathrm{\pi }}$ 4. $\mathrm{\alpha }=12.50$ $\mathrm{\pi },$ $\mathrm{\beta }=\frac{\mathrm{\pi }}{2.0}$

Subtopic:  Wave Motion |
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In an experiment with a sonometer, a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. If the tension of the string remains constant, then the frequency of the second tuning fork will be:

1. 163.84 Hz

2. 400 Hz

3. 320 Hz

4. 204.8 Hz

Subtopic:  Standing Waves |
74%
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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:  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:  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:  Energy of Waves |
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Two progressive waves are represented by, $$y_1=5sin(200t-3.14x)$$ and
$$y_2=10sin(200t-3.14x+\frac{\pi}{3})$$
($$x$$ is in metres, and $$t$$ is in seconds). Path difference between the two waves is:
1.

2.

3.

4.

Subtopic:  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 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:  Wave Motion |
85%
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A cylindrical tube open at both ends has a fundamental frequency f0 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. $\frac{3{f}_{\mathit{0}}}{4}$

2. ${f}_{0}$

3. $\frac{{f}_{\mathit{0}}}{2}$

4. 2${f}_{0}$

Subtopic:  Standing Waves |
68%
From NCERT
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The equation of a stationary wave is given as $\mathrm{y}=\mathrm{A}$ $\mathrm{sin}$ $0.5\mathrm{\pi t}$ $\mathrm{cos}\left(0.2\mathrm{\pi x}\right),$  where t is in seconds and x in centimetres. Which of the following is correct?

 1 Wavelength of the component waves is 10 cm. 2 The separation between a node and the nearest antinode is 2.5 cm. 3 Frequency of the component wave is 0.25 Hz. 4 All of these

Subtopic:  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 Hz

2. 63 Hz

3. 126 Hz

4. 168 Hz

Subtopic:  Standing Waves |
76%
From NCERT
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