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Ch 16: Traveling Waves
All textbooksKnight Calc 5th EditionCh 16: Traveling WavesProblem 17
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Chapter 16, Problem 17

FIGURE EX17.6 shows a standing wave oscillating at 100 Hz on a string. What is the wave speed? Diagram of a standing wave on a string, oscillating at 100 Hz, with a length of 72 cm.

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Identify the given information: the frequency of the standing wave is 100 Hz and the length of the string is 72 cm.
Count the number of wavelengths in the standing wave. From the image, there are 3 complete wavelengths.
Calculate the wavelength (λ) by dividing the length of the string by the number of wavelengths. λ = 72 cm / 3.
Convert the wavelength from cm to meters if necessary.
Use the wave speed formula v = f * λ, where f is the frequency and λ is the wavelength, to find the wave speed.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 (lambda) is the wavelength. In this case, the frequency is given as 100 Hz, and the wavelength can be determined from the standing wave pattern shown in the figure.
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Standing Waves

A standing wave is formed when two waves of the same frequency and amplitude travel in opposite directions and interfere with each other. This results in nodes (points of no displacement) and antinodes (points of maximum displacement) along the medium. The length of the string and the number of wavelengths it contains are crucial for determining the wavelength in this scenario.
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Wavelength

Wavelength is the distance between successive crests (or troughs) of a wave. For standing waves, the wavelength can be calculated based on the length of the string and the number of loops formed. In this case, the string length of 72 cm can be used to find the wavelength, which is essential for calculating the wave speed.
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Textbook Question
A violinist places her finger so that the vibrating section of a 1.0 g/m string has a length of 30 cm, then she draws her bow across it. A listener nearby in a 20°C room hears a note with a wavelength of 40 cm. What is the tension in the string?
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Textbook Question
INT One end of a 75-cm-long, 2.5 g guitar string is attached to a spring. The other end is pulled, which stretches the spring. The guitar string's second harmonic occurs at 550 Hz when the spring has been stretched by 5.0 cm. What is the value of the spring constant?
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A string under tension has a fundamental frequency of 220 Hz. What is the fundamental frequency if the tension is doubled?
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a. What are the three longest wavelengths for standing waves on a 60 cm long string that is fixed at both ends?
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Textbook Question
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Textbook Question
The two highest-pitch strings on a violin are tuned to 440 Hz (the A string) and 659 Hz (the E string). What is the ratio of the mass of the A string to that of the E string? Violin strings are all the same length and under essentially the same tension.
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