When a standing wave is set up on a string fixed at both ends, which of the following statements is true?
Correct answer: C. The shape of the string at any instant shows a symmetry about the midpoint of the string
- A. Sum of the number of antinodes and the number of nodes is always even
- B. Wavelength = length string / number of nodes
- C. The shape of the string at any instant shows a symmetry about the midpoint of the string
- D. Frequency = number of nodes x fundamental frequency
Explanation
A string plucked from 1/2 of the length or any of the further harmonics shows symmetry about it's midpoint, if the wave pattern is divided into two equal parts, then it is observed that they are symmetrical. The frequency of such wave is given by ω/2π.
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About Waves
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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