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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
Capitolo 15, Problema 50

The speed of waves on a string is 96 m/s. If the frequency of standing waves is 435 Hz, how far apart are two adjacent nodes?

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Step 1: Recall the relationship between wave speed, frequency, and wavelength. The formula is: v = fλ, where v is the wave speed, f is the frequency, and λ is the wavelength.
Step 2: Rearrange the formula to solve for the wavelength: λ = vf. Substitute the given values for wave speed (v = 96 m/s) and frequency (f = 435 Hz) into the equation.
Step 3: Calculate the wavelength λ. This represents the distance between two consecutive points in phase on the wave, such as two crests or two troughs.
Step 4: Recall that the distance between two adjacent nodes in a standing wave is half the wavelength. Use the relationship: d = λ2, where d is the distance between adjacent nodes.
Step 5: Substitute the calculated wavelength into the formula for d to determine the distance between adjacent nodes.

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Wave Speed

Wave speed is the distance traveled by a wave per unit time, calculated as the product of frequency and wavelength. In this case, the speed of waves on the string is given as 96 m/s, which is essential for determining the relationship between frequency and wavelength in standing waves.
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Intro to Waves and Wave Speed

Frequency

Frequency is the number of cycles of a wave that pass a point in one second, measured in hertz (Hz). In the question, the frequency of the standing waves is 435 Hz, which indicates how many complete wave cycles occur each second, influencing the wavelength and the distance between nodes.
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Nodes and Wavelength

Nodes are points along a standing wave where the wave has minimal amplitude, occurring at regular intervals. The distance between two adjacent nodes is half the wavelength. By using the relationship between wave speed, frequency, and wavelength, one can calculate the distance between nodes in the standing wave.
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