Learning Goal:To understand standing waves, including calculation of X andf, and to learn the physical meaning behind some musicalterms.The columns in the figure (Figure 1) show the instantaneousshape of a vibrating guitar string drawn every 1 ms. Theguitar string is 60 cm long.The left column shows the guitar string shape as a sinusoidaltraveling wave passes through it. Notice that the shape issinusoidal at all times and specific features, such as the crestindicated with the arrow, travel along the string to the right ata constant speed.The right column shows snapshots of the sinusoidal standingwave formed when this sinusoidal traveling wave passesthrough an identically shaped wave moving in the oppositedirection on the same guitar string. The string is momentarilyflat when the underlying traveling waves are exactly out ofphase. The shape is sinusoidal with twice the originalamplitude when the underlying waves are momentarily innhaco Thic nattern is called a standing wave heralice.noFigureTime Traveling Wave0 ms.1 ms.2 ms3 msyIx=0cmStanding Wave1 of 3 >BIS.Ix= x=60 cm 0 cmx=XX60 cmWaves of all wavelengths travel at the same speed v on a given string. Traveling wave velocity and wavelength are related byv=Xf.where v is the wave speed (in meters per second), A 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 standingwave series. The frequency of the nth pattern isfn == (2L/n) = nz=Note that the frequency of the fundamental is f₁ = v/(2L), so f₁ can also be thought of as an integer multiple of fi: fn = nf₁.Part CThe 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.▸ View Available Hint(s)v=SubmitVE ΑΣΦ 1Part D Complete previous part(s)Part E Complete previous part(s)Provide Feedbackpe?m/sNext >

Given data: Fundamental frequency (f1) = 320 Hz Length (L) = 60 cm = 0.60 m Required: The wave…

Part C The frequency of the fundamental of the guitar string is 320 Hz. At what speed do waves move along that string? Express your answer in meters per second. ▸ View Available Hint(s) V= [1] ΑΣΦ yg ? m/s.

Part C The frequency of the fundamental of the guitar string is 320 Hz. At what speed do waves move along that string? Express your answer in meters per second. ▸ View Available Hint(s) V= [1] ΑΣΦ yg ? m/s.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Wave Motion

A wave motion is defined as the propagation of disturbances or transfer of energy and momentum from the state of rest or equilibrium to another point in a medium without any actual transfer of matter between them. In a simple explanation, it is the propagation of energy through a medium that is produced due to the repeated vibrations of the particles. Common things we see day to day like waves on water oscillation of a pendulum or bell, light wave, and all the subatomic particles exhibiting wavelike properties. The propagation of waves depends on the medium and their properties. The wave function is the disturbance that produces waves as a function of time. This disturbance oscillates periodically with a fixed frequency and wavelength. There are linear wave motion and non-linear wave motion based on their propagation, motion, and time period where linear wave motion is like sinusoidal waves and non-linear wave motion like a wave motion that gets interrupted in the middle of their propagation.

Question

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
nhaco Thic nattern is called a standing wave heralice.no
Figure
Time Traveling Wave
0 ms.
1 ms.
2 ms
3 ms
y
I
x=
0cm
Standing Wave
1 of 3 >
BIS.
I
x= x=
60 cm 0 cm
x=
X
X
60 cm
Waves of all wavelengths travel at the same speed v on a given string. Traveling wave velocity and wavelength are related by
v=Xf.
where v is the wave speed (in meters per second), A 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 == (2L/n) = nz
=
Note that the frequency of the fundamental is f₁ = v/(2L), so f₁ can also be thought of as an integer multiple of fi: 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.
▸ View Available Hint(s)
v=
Submit
VE ΑΣΦ 1
Part D Complete previous part(s)
Part E Complete previous part(s)
Provide Feedback
pe
?
m/s
Next >

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