Consider a standing wave, where y represents the transverse displacement of a string that extends along the x direction. Here is a common mathematical form for such a wave: y(x, t) = A cos(kæ) sin(wt), where A is the maximum transverse displacement of the string (the amplitude of the wave), which is assumed to be nonzero, k is the wavenumber, w is the angular frequency of the wave, and t is time.
Consider a standing wave, where y represents the transverse displacement of a string that extends along the x direction. Here is a common mathematical form for such a wave: y(x, t) = A cos(kæ) sin(wt), where A is the maximum transverse displacement of the string (the amplitude of the wave), which is assumed to be nonzero, k is the wavenumber, w is the angular frequency of the wave, and t is time.
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Transcribed Image Text:Consider a standing wave, where y represents the
transverse displacement of a string that extends
along the x direction. Here is a common
mathematical form for such a wave:
y(x, t) = A cos(ka) sin(wt),
where A is the maximum transverse displacement
of the string (the amplitude of the wave), which is
assumed to be nonzero, k is the wavenumber, w is
the angular frequency of the wave, and t is time.
Transcribed Image Text:At which three points x1, x2, and x3 closest to x = 0 but with x > 0 will the displacement
of the string y (x,t) be zero for all times? These are the first three nodal points.
Express the first three nonzero nodal points as multiples of the wavelength A, using
constants like T. List the factors that multiply A in increasing order, separated by
commas.
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