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Ch. 15 - Wave Motion
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoGiancoli Douglas 5th editionCh. 15 - Wave MotionProblema 63
Capitolo 15, Problema 63

When you slosh the water back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 45-cm-wide tub is 0.85 Hz. What is the speed of the water wave?

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Identify the relationship between the frequency, wavelength, and wave speed. The formula to use is: v=fλ, where v is the wave speed, f is the frequency, and λ is the wavelength.
Recognize that the standing wave in the tub corresponds to the fundamental mode of oscillation. In this mode, the wavelength λ is twice the width of the tub. Thus, calculate the wavelength as: λ=2×0.45=0.90m.
Substitute the given frequency f=0.85Hz and the calculated wavelength λ=0.90m into the wave speed formula: v=fλ.
Perform the multiplication to find the wave speed: v=0.85×0.90. This will give the speed of the water wave in meters per second.
Ensure the units are consistent throughout the calculation (meters for wavelength, Hz for frequency, and m/s for speed) and verify the result for accuracy.

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Wave Speed

Wave speed is the distance a wave travels per unit of time. It can be calculated using the formula v = fλ, where v is the wave speed, f is the frequency, and λ is the wavelength. In the context of standing waves, understanding wave speed is crucial for determining how quickly the wave propagates through the medium, which in this case is water.
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07:19
Intro to Waves and Wave Speed

Standing Waves

Standing waves occur when two waves of the same frequency and amplitude travel in opposite directions and interfere with each other. This results in specific points called nodes, where there is no movement, and antinodes, where the movement is maximum. In the given scenario, the water in the tub creates a standing wave pattern due to the sloshing motion at a specific frequency.
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Intro to Transverse Standing Waves

Frequency and Wavelength Relationship

The relationship between frequency and wavelength is fundamental in wave mechanics. For waves, the frequency (f) is inversely related to the wavelength (λ) when the wave speed (v) is constant, expressed as v = fλ. In this problem, knowing the frequency allows us to find the wave speed, provided we can determine the wavelength of the standing wave in the tub.
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Circumference, Period, and Frequency in UCM
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