SOLVED:What Happens To The Wavelength Of A Wave On ... - Numerade

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What happens to the wavelength of a wave on a string when the frequency is doubled? What happens to the speed of the wave? What happens to the wavelength of a wave on a string when the frequency is doubled? What happens to the speed of the wave? Physics Raymond A. Serway,… 1st Edition Chapter 11, Problem 30 View All Chapters

Step 1

This relationship is given by the equation: \[ v = \lambda f \] where \( v \) is the speed of the wave, \( \lambda \) is the wavelength, and \( f \) is the frequency. Show more…

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Key Concepts

Wavelength Wavelength is the distance between consecutive points that are in phase, such as crest to crest. Under a constant wave speed, increasing the frequency results in a proportionate decrease in wavelength. Medium Properties and Wave Speed The speed of a wave on a string is determined by the physical properties of the medium, such as tension and mass density. If these properties remain unchanged, the wave speed stays constant even when the frequency is altered. Wave Equation (v = f?) This fundamental relationship in wave mechanics dictates that the speed (v) of a wave is the product of its frequency (f) and wavelength (?). When the wave speed remains constant, any change in frequency results in an inverse change in wavelength. Frequency Frequency is the measure of how many cycles or oscillations occur per unit time. It plays a key role in determining the wavelength of a wave when the wave speed is fixed.

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Transcript

00:01 So we're asked about a wave and the frequency of the wave is doubled. 00:06 What happens to the wavelength as a result and what happens to the speed of that wave? we're going to derive the speed of a wave. 00:14 We know that speed is the distance or the displacement traveled per unit time. 00:24 We have to choose our values carefully to come up with an equation. 00:28 So we know a few things from our previous videos. 00:32 The period, which is the time it takes for one cycle. 00:41 And also we have the wavelength, which is the length of a cycle. 01:03 Time is units of seconds and wave lengths and units of meters. 01:14 So if we were to have a wave pass or traverse for one period, one full period, that means there would be one full cycle that travels. 01:25 And in one full cycle, there's a length of lambda that is passed. 01:31 So for this equation, we can write lambda as our displacement or our distance traveled and the period as the time traveled. 01:44 This is a correct expression... Need help? Use Ace Ace is your personal tutor. It breaks down any question with clear steps so you can learn. Start Using Ace Ace is your personal tutor for learning Step-by-step explanations Instant summaries Summarize YouTube videos Understand textbook images or PDFs Study tools like quizzes and flashcards Listen to your notes as a podcast

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