# The displacement of a particle is given by $y=5×{10}^{-4}\mathrm{sin}\left(100t-50x\right)$, <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> where x is in metres and t is in seconds. The velocity of the wave is: 1. 5000 m/sec 2. 2 m/sec 3. 0.5 m/sec 4. 300 m/sec

Subtopic:  Wave Motion |
89%
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The wave equations of two particles are given by ${y}_{1}=a\mathrm{sin}\left(\omega \text{\hspace{0.17em}}t-kx\right)$, ${y}_{2}=a\mathrm{sin}\left(kx+\omega \text{\hspace{0.17em}}t\right)$, then:

 1 they are moving in the opposite direction. 2 the phase between them is 90°. 3 the phase between them is 45°. 4 the phase between them is 0°.
Subtopic:  Wave Motion |
79%
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The equation of a progressive wave is given by $y=4\mathrm{sin}\left\{\pi \left(\frac{t}{5}-\frac{x}{9}\right)+\frac{\pi }{6}\right\}$.
Which of the following is correct​​​​?
1. v = 5 m / sec
2.  λ = 18 m
3.  a = 0.04 m
4.  n = 50 Hz

Subtopic:  Wave Motion |
85%
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Two waves are propagating to the point P along a straight line produced by two sources, A and B, of simple harmonic and equal frequency. The amplitude of every wave at P is ‘a’ and the phase of A is ahead by π/3 than that of B, and the distance AP is greater than BP by 50 cm. If the wavelength is 1 meter, then the resultant amplitude at point P will be:
1. 2a
2. $a\sqrt{3}$
3. $a\sqrt{2}$
4. a

Subtopic:  Standing Waves |
From NCERT
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Tuning fork $$F_1$$ has a frequency of 256 Hz and it is observed to produce 6 beats/second with another tuning fork $$F_2$$. When $$F_2$$ is loaded with wax, it still produces 6 beats/second with $$F_1$$. The frequency of $$F_2$$ before loading was:
1. 253 Hz
2. 262 Hz
3. 250 Hz
4. 259 Hz

Subtopic:  Beats |
70%
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Two tuning forks, A and B, vibrating simultaneously produce 5 beats. The frequency of B is 512 Hz. It is seen that if one arm of A is filed a little, then the number of beats increases. The frequency of A in Hz will be:

 1 502 2 507 3 517 4 522
Subtopic:  Beats |
69%
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The equation of a stationary wave is $$y = 0.8 ~cos\left(\frac{\pi x}{20}\right)sin200(\pi t)$$, where $$x$$ is in cm and $$t$$ is in sec. The separation between consecutive nodes will be:

1. $$20~\text{cm}$$

2. $$10~\text{cm}$$

3. $$40~\text{cm}$$

4. $$30~\text{cm}$$

Subtopic:  Standing Waves |
76%
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A closed pipe and an open pipe have their first overtones identical in frequency. Their lengths are in the ratio:

 1 1 : 2 2 2 : 3 3 3 : 4 4 4 : 5
Subtopic:  Standing Waves |
73%
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Three waves of equal frequency having amplitudes of 10 μm, 4 μm and 7 μm arrive at a given point with a successive phase difference of $\frac{\pi }{2}$. The amplitude of the resulting wave in μm is given by:
1. 7
2. 6
3. 5
4. 4

Subtopic:  Standing Waves |
60%
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An organ pipe that is closed at one end has a fundamental frequency of 1500 Hz. The maximum number of overtones generated by this pipe that a normal person can hear is:

 1 14 2 13 3 6 4 9
Subtopic:  Standing Waves |
59%
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