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Learning Goal: To understand standing waves, including calculation of A and f, and to learn the physical meaning behind some musical terms. The columns in the figure (Figure 1) show the instantaneous shape of a vibrating guitar string drawn every 1 ms. The guitar string is 60 cm long. The left column shows the guitar string shape as a sinusoidal traveling wave passes through it. Notice that the shape is sinusoidal at all times and specific features, such as the crest indicated with the arrow, travel along the string to the right at a constant speed. The right column shows snapshots of the sinusoidal standing wave formed when this sinusoidal traveling wave passes through an identically shaped wave moving in the opposite direction on the same guitar string. The string is momentarily flat when the underlying traveling waves are exactly out of phase. The shape is sinusoidal with twice the original amplitude when the underlying waves are momentarily in This figure(Figure 3) shows the first three standing wave patterns that fit on any string with length L tied down at both ends. A pattern's number n is the number of antinodes it contains. The wavelength of the nth pattern is denoted An. The nth pattern has n half-wavelengths along the length of the string, so L Thus the wavelength of the nth pattern is Part B What is the wavelength of the longest wavelength standing wave pattern that can fit on this guitar string? Express your answer in centimeters. ▸ View Available Hint(s) [V] ΑΣΦ A₁ = 2L TL ?

Learning Goal: To understand standing waves, including calculation of A and f, and to learn the physical meaning behind some musical terms. The columns in the figure (Figure 1) show the instantaneous shape of a vibrating guitar string drawn every 1 ms. The guitar string is 60 cm long. The left column shows the guitar string shape as a sinusoidal traveling wave passes through it. Notice that the shape is sinusoidal at all times and specific features, such as the crest indicated with the arrow, travel along the string to the right at a constant speed. The right column shows snapshots of the sinusoidal standing wave formed when this sinusoidal traveling wave passes through an identically shaped wave moving in the opposite direction on the same guitar string. The string is momentarily flat when the underlying traveling waves are exactly out of phase. The shape is sinusoidal with twice the original amplitude when the underlying waves are momentarily in This figure(Figure 3) shows the first three standing wave patterns that fit on any string with length L tied down at both ends. A pattern's number n is the number of antinodes it contains. The wavelength of the nth pattern is denoted An. The nth pattern has n half-wavelengths along the length of the string, so L Thus the wavelength of the nth pattern is Part B What is the wavelength of the longest wavelength standing wave pattern that can fit on this guitar string? Express your answer in centimeters. ▸ View Available Hint(s) [V] ΑΣΦ A₁ = 2L TL ?

University Physics Volume 1
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter16: Waves
Section: Chapter Questions
Problem 27CQ: Many of the topics discussed in this chapter are useful beyond the topics of mechanical waves. It is...
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Learning Goal: To understand standing waves, including calculation of A and f, and to learn the physical meaning behind some musical terms. The columns in the figure (Figure 1) show the instantaneous shape of a vibrating guitar string drawn every 1 ms. The guitar string is 60 cm long. The left column shows the guitar string shape as a sinusoidal traveling wave passes through it. Notice that the shape is sinusoidal at all times and specific features, such as the crest indicated with the arrow, travel along the string to the right at a constant speed. The right column shows snapshots of the sinusoidal standing wave formed when this sinusoidal traveling wave passes through an identically shaped wave moving in the opposite direction on the same guitar string. The string is momentarily flat when the underlying traveling waves are exactly out of phase. The shape is sinusoidal with twice the original amplitude when the underlying waves are momentarily in Figure Time Traveling Wave 0 ms 1 ms 2 ms 3 ms I x= 0cm Standing Wave 1$1$= x= x= 60 cm 0 cm 1 of 3 > X 60 cm This figure(Figure 3) shows the first three standing wave patterns that fit on any string with length I tied down at both ends. A pattern's number is the number of antinodes it contains. The wavelength of the nth pattern is denoted An. The nth pattern has n half-wavelengths along the length of the string, so n²/2 = L. An = 2L Thus the wavelength of the nth pattern is Part B What is the wavelength of the longest wavelength standing wave pattern that can fit on this guitar string? Express your answer in centimeters. ► View Available Hint(s) A₁ = Submit 15. ΑΣΦ Part C Complete previous part(s) Part D Complete previous part(s) Part E Complete previous part(s) Provide Feedback aww ? cm Next >
Transcribed Image Text:Learning Goal: To understand standing waves, including calculation of A and f, and to learn the physical meaning behind some musical terms. The columns in the figure (Figure 1) show the instantaneous shape of a vibrating guitar string drawn every 1 ms. The guitar string is 60 cm long. The left column shows the guitar string shape as a sinusoidal traveling wave passes through it. Notice that the shape is sinusoidal at all times and specific features, such as the crest indicated with the arrow, travel along the string to the right at a constant speed. The right column shows snapshots of the sinusoidal standing wave formed when this sinusoidal traveling wave passes through an identically shaped wave moving in the opposite direction on the same guitar string. The string is momentarily flat when the underlying traveling waves are exactly out of phase. The shape is sinusoidal with twice the original amplitude when the underlying waves are momentarily in Figure Time Traveling Wave 0 ms 1 ms 2 ms 3 ms I x= 0cm Standing Wave 1$1$= x= x= 60 cm 0 cm 1 of 3 > X 60 cm This figure(Figure 3) shows the first three standing wave patterns that fit on any string with length I tied down at both ends. A pattern's number is the number of antinodes it contains. The wavelength of the nth pattern is denoted An. The nth pattern has n half-wavelengths along the length of the string, so n²/2 = L. An = 2L Thus the wavelength of the nth pattern is Part B What is the wavelength of the longest wavelength standing wave pattern that can fit on this guitar string? Express your answer in centimeters. ► View Available Hint(s) A₁ = Submit 15. ΑΣΦ Part C Complete previous part(s) Part D Complete previous part(s) Part E Complete previous part(s) Provide Feedback aww ? cm Next >
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