Standing Wave in String and Organ Pipe

Question 1:
In a stationary wave all the particles

On either side of a node vibrate in same phase

In the region between two nodes vibrate in same phase

In the region between two antinodes vibrate in same phase

Of the medium vibrate in same phase

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No solution provided for this question.

Question 2:
The particle displacement (in cm) in a stationary wave is given by y(x, t) = 2 sin (0.1 πx) cos (100 πt). The distance between a node and the next antinode is

2.5 cm

7.5 cm

5 cm

10 cm

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No solution provided for this question.

Question 3:
Two wires are kept tight between the same pairof support. The tensions in the wires are in the ratio 2 : 1, the radii are in the ratio 3 : 1 and the densities are in the ratio 1 : 2. The ratio of their fundamental frequencies is

2 : 3

2 : 4

2 : 5

2 : 6

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No solution provided for this question.

Question 4:
The fundamental frequency of a closed pipe is 220 Hz. If 1/4 of the pipe is filled with water, the frequency of the first overtone of the pipe now is

220 Hz

440 Hz

880 Hz

1760 Hz

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No solution provided for this question.

Question 5:
An organ pipe P1 closed at one vibrating in its first overtone and another pipe P2 open at both ends vibrating in third overtone are in resonance with a given tuning fork. The ratio of the length of P1 to that of P2 is

3/8

8/3

1/2

1/3

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No solution provided for this question.

Question 6:
A second harmonic has to be generated in a string of length l stretched between two rigid supports. The point where the string has to be plucked and touched are

Plucked at l/4 and touch at l/2

Plucked at l/4 and touch at 3l/4

Plucked at l/2 and touched at l/4

Plucked at l/2 and touched at 3l/4

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No solution provided for this question.