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 (Eigure 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 phase. This pattern is called a standing wave because no wave features travel down the length of the string. Figure Time Traveling Wave 0 ms 1 ms 2 ms 3 ms X= 0cm Standing Wave TIBIS < 1 of 2 > xw x= 60 cm 0 cm xw 60 cm Standing waves on a guitar string form when waves traveling down the string reflect off a point where the string is tied down or pressed against the fingerboard. The entire series of distortions may be superimposed on a single figure, like this (Eigure 2), indicating different moments in time using traces of different colors or line styles. Y Part A What is the wavelength A of the standing wave shown on the guitar string? Express your answer in centimeters. ▸ View Available Hint(s) A= Submit | ΑΣΦ ΑΣΦΑ Part B Complete previous part(s) Part C Complete previous part(s) Part D Complete previous part(s) Part E Complete previous part(s) Provide Feedback ? cm Next >
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 (Eigure 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 phase. This pattern is called a standing wave because no wave features travel down the length of the string. Figure Time Traveling Wave 0 ms 1 ms 2 ms 3 ms X= 0cm Standing Wave TIBIS < 1 of 2 > xw x= 60 cm 0 cm xw 60 cm Standing waves on a guitar string form when waves traveling down the string reflect off a point where the string is tied down or pressed against the fingerboard. The entire series of distortions may be superimposed on a single figure, like this (Eigure 2), indicating different moments in time using traces of different colors or line styles. Y Part A What is the wavelength A of the standing wave shown on the guitar string? Express your answer in centimeters. ▸ View Available Hint(s) A= Submit | ΑΣΦ ΑΣΦΑ Part B Complete previous part(s) Part C Complete previous part(s) Part D Complete previous part(s) Part E Complete previous part(s) Provide Feedback ? cm Next >
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Question
Transcribed Image Text:Item 6
Learning Goal:
To understand standing waves, including calculation of X 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 phase. This pattern is called a
standing wave because no wave features travel down the length of the
string.
Figure
Time Traveling Wave
0 ms
1 ms
2 ms
3 ms
I
X=
0cm
Standing Wave
X= X=
60 cm 0 cm
➤X
X
X=
60 cm
1 of 2
▶
Part A
What is the wavelength of the standing wave shown on the guitar string?
Express your answer in centimeters.
► View Available Hint(s)
Standing waves on a guitar string form when waves traveling down the string reflect off a point where the string is tied down or pressed against the fingerboard. The entire series of
distortions may be superimposed on a single figure, like this (Figure 2), indicating different moments in time using traces of different colors or line styles.
λ =
Submit
VE ΑΣΦ
Part B Complete previous part(s)
Part C Complete previous part(s)
Part D Complete previous part(s)
Part E Complete previous part(s)
Provide Feedback
?
<
cm
6 of 15
Review
Next >
Expert Solution
Introduction:
We are given length of guitar. We are given the standing wave produced in the figure. We first see how many waves are being fit inside this length of the guitar. The length of all these waves that are fit is equal to length of guitar. We hence find wavelength of standing wave.
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