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The equation of a wave travelling on a string is y = sin [20πx + 10πt], where x and t are distance and time in SI units. The minimum distance between two points having same oscillating speed is : (1) 10 cm (2) 2.5 cm (3) 20 cm (4) 5.0 cm

1. 10 cm
2. 2.5 cm
3. 20 cm
4. 5.0 cm

Correct answer: 5.0 cm

Solution

The wave equation indicates that the wave has a wavelength of 20 cm, which means that points on the wave that oscillate in phase (having the same speed) are separated by half the wavelength. Therefore, the minimum distance between two points with the same oscillating speed is 5.0 cm.

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