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singletaryshawp31cmx
29.10.2019 •
Physics
Athin taut string is fixed at both ends and stretched along the horizontal x-axis with its left end at x = 0. it is vibrating in its third overtone, and the equation for the vertical displacement of any point on the string is y(x,t) = (1.22 cm) sin[(14.4 m-1)x] cos[(166 rad/s)t]. (a) what are the frequency and wavelength of the fundamental mode of this string? (b) how long is the string? (c) how fast do waves travel on this string?
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Ответ:
(a) Wavelength is 0.436 m
(b) Length is 0.872 m
(c) 11.518 m/s
Solution:
As per the question:
The eqn of the displacement is given by:
n = 4
Now,
We know the standard eqn is given by:
Now, on comparing eqn (1) and (2):
A = 1.22 cm
K =![14.4 m^{- 1}](/tpl/images/0350/7461/cf400.png)
where
A = Amplitude
K = Propagation constant
Now, to calculate the string's wavelength,
(a)![K = \frac{2\pi}{\lambda}](/tpl/images/0350/7461/75b07.png)
where
K = propagation vector
(b) The length of the string is given by:
(c) Now, we first find the frequency of the wave:
Now,
Speed of the wave is given by:
Ответ: