A transverse wave on a string has an amplitude A. A tiny spot on the string is coloured red. As 1.5 cycle of the wave passes by, what is the total distance travelled by the red spot?
Correct answer: D. 6A
- A. A
- B. 2A
- C. 4A
- D. 6A
Explanation
The particles in a transverse wave oscillate periodically in a direction perpendicular to the propagation of the wave. This means that the string is undergoing SHM. For simple harmonic motion, one complete cycle is equal to 4 times the amplitude. One cycle goes as follows; Upward movement, Downward movement, then again Upward in the opposite direction, and finally back to its mean position, completing a total distance of 4A. If, 1 cycle = 4A Then, 1.5 cycle = x x = 1.4 × 4A x = 56/10 A x = 5.6A ~ 6A
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Progressive waves transfer energy through oscillations, with wavelength, frequency, amplitude and wave speed related by v = fλ; sound speed depends on the medium. Superposition produces interference and stationary waves in strings and organ pipes, while simple harmonic motion describes the oscillation itself and must be distinguished from wave propagation.
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