A string of length 0.60 m is stretched between two fixed points. When plucked, it vibrates in its fundamental mode at a frequency of 250 Hz.

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Key answer: in the fundamental mode the string carries half a wavelength, so λ = 2L = 1.2 m v = fλ = 250 × 1.2 v = 300 m s⁻¹ in the fundamental mode the string carries half a wavelength, so λ = 2L = 1.2 m v = fλ = 250 × 1.2 v = 300 m s⁻¹ a wave travels along the string and reflects at the fixed end, and the reflected wave travels back along the string the two waves have the same frequency, speed and amplitude and travel in opposite directions, so they superpose the superposition produces fixed nodes where the two always cancel and antinodes where they always reinforce a standing wave transfers no energy along the string, and every point between adjacent nodes oscillates in phase — unlike a progressive wave, in which phase changes steadily along the direction of travel f₃ = 3 × 250 = 750 Hz The third harmonic has four displacement nodes, including both fixed ends. the wave speed on a string increases with tension, so v rises the wavelength of the fundamental is fixed at 2L by the geometry, so f = v/λ increases the speed depends only on the tension and the mass per unit length of the string — properties of the medium — and not on how much of that medium is between the supports

Wave behaviour · Question 8

A string of length 0.60 m is stretched between two fixed points. When plucked, it vibrates in its fundamental mode at a frequency of 250 Hz.

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