Pregunta
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\begin{tabular}{|l}\hline Faster or slower wave speed? \\ A. The medium gets colder. \\ B. The amplitude gets bigger. \\ C. A slinky gets looser. \\ D. The medium turns from solid to liquid. \\ E. The wavelength gets shorter. \\ Wave 1: \( \mathrm{f}=25 \mathrm{~Hz} \); Wave \( 2: \mathrm{f}=40 \mathrm{~Hz} \). Which one will be faster \\ in water? \end{tabular}

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Mar 12,2025

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Wave 2 with a frequency of 40 Hz will be faster in water.

Solución

To determine which wave will be faster in water, we need to consider the relationship between wave speed and frequency. The speed of a wave in a medium is given by the formula: \[ v = f \times \lambda \] where: - \( v \) is the speed of the wave, - \( f \) is the frequency of the wave, and - \( \lambda \) is the wavelength of the wave. Given that the frequency of Wave 1 is 25 Hz and the frequency of Wave 2 is 40 Hz, we can compare their speeds in water by considering the relationship between frequency and wave speed. Since the frequency of Wave 2 (40 Hz) is higher than that of Wave 1 (25 Hz), Wave 2 will have a higher speed in water. Therefore, Wave 2 will be faster in water.

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Beyond the Answer

When discussing wave speed, it's important to note that the speed of a wave is influenced by the properties of the medium through which it travels. In general, as the medium turns from solid to liquid (option D), wave speed decreases because liquids are less dense and more compressible than solids, thus impeding wave propagation. Meanwhile, temperature affects wave speed in liquids, with colder mediums typically resulting in slower wave speeds as the molecules move less vigorously. For your question about wave speed in water, remember that frequency doesn't change the speed of a wave in a given medium but rather determines wavelength. In water, the speed of sound (and therefore wave speed) is largely constant regardless of frequency. Thus, waves travel at the same speed in water irrespective of their frequency of 25 Hz or 40 Hz. However, higher frequency waves can have shorter wavelengths, but speed remains constant.

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