Question

Standing Waves on a Guitar String Learning Goal: To understand standing waves, including calculation of ? 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. Waves of all wavelengths travel at the same speed v on a given string. Traveling wave velocity and wavelength are related by v = ?f, where v is the wave speed (in meters per second), ? is the wavelength (in meters), and f is the frequency [in inverse seconds, also known as hertz (Hz)]. Since only certain wavelengths fit properly to form standing waves on a specific string, only certain frequencies will be represented in that string's standing wave series. The frequency of the nth pattern is f_n = v/?_n = v/(2L/n) = n(v/2L). Note that the frequency of the fundamental is f_1 = v/(2L), so f_n can also be thought of as an integer multiple of f_1: f_n = nf_1. Part C The frequency of the fundamental of the guitar string is 320 Hz. At what speed v do waves move along that string? Express your answer in meters per second. v = 128 m/s

          Standing Waves on a Guitar String
Learning Goal:
To understand standing waves, including calculation of ? 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.
Waves of all wavelengths travel at the same speed v on a given string. Traveling wave velocity and wavelength are related by
v = ?f,
where v is the wave speed (in meters per second), ? is the wavelength (in meters), and f is the frequency [in inverse seconds, also known as hertz (Hz)].
Since only certain wavelengths fit properly to form standing waves on a specific string, only certain frequencies will be represented in that string's standing wave series. The frequency of the nth pattern is
f_n = v/?_n = v/(2L/n) = n(v/2L).
Note that the frequency of the fundamental is f_1 = v/(2L), so f_n can also be thought of as an integer multiple of f_1:
f_n = nf_1.
Part C
The frequency of the fundamental of the guitar string is 320 Hz. At what speed v do waves move along that string?
Express your answer in meters per second.
v = 128 m/s

Standing Waves on a Guitar String
Learning Goal:
To understand standing waves, including calculation of ? 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.
Waves of all wavelengths travel at the same speed v on a given string. Traveling wave velocity and wavelength are related by
v = ?f,
where v is the wave speed (in meters per second), ? is the wavelength (in meters), and f is the frequency [in inverse seconds, also known as hertz (Hz)].
Since only certain wavelengths fit properly to form standing waves on a specific string, only certain frequencies will be represented in that string's standing wave series. The frequency of the nth pattern is
fn = v/?n = v/(2L/n) = n(v/2L).
Note that the frequency of the fundamental is f1 = v/(2L), so fn can also be thought of as an integer multiple of f1:
fn = nf1.
Part C
The frequency of the fundamental of the guitar string is 320 Hz. At what speed v do waves move along that string?
Express your answer in meters per second.
v = 128 m/s

Added by Enrique G.

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