Please help. I need clear answers for each letter. The equation of a transverse
ID: 1306521 • Letter: P
Question
Please help. I need clear answers for each letter.
The equation of a transverse wave traveling along a very long string is y = 7.0 sin (0.045 nx + 6.0 nt), where x and y are expressed in centimeters and t is in seconds.
(a) Determine the amplitude of propagation of the wave.
(b) Determine the wavelength of the wave
(c) Determine the frequency of the wave
(d) Determine the speed of the wave
(e) Determine the direction of propagation of the wave along the x-axis. (ie. Positive or Negative?)
(f) Determine the maximum transverse speed of a particle in the string.
(g) What is the transverse displacement at x = 4.60 cm when t = 0.38 s?
Explanation / Answer
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The equation of a transverse wave traveling along a very longstring is y=6.0sin(0.020?x + 4.0?t), where x and y areexpressed in centimeters and t is in seconds. Determine a)the amplitude, b)the wavelength, c) the frequency, d) thespeed,
e) the direction of propagation of the wave, and f) the maximumtransverse speed of a particle in the string. g) What is thetransverse displacement at x = 3.5 cm when t = 0.26 s?
answer
given
y=6.0sin(0.020?x + 4.0?t)
the general wave equation moving in the positive directionis
y(x,t) = ymsin(kx -?t)
a) the amplitude is
ym = 6.0cm
b)
we have the angular wave number as
k = 2? /?
or
? = 2? / 0.020?
=1.0*102cm
c)
the frequency is
f = ?/2?
= 4?/2?
= 2.0 Hz
d)
the wave speed is
v = f?
= (100cm)(2.0Hz)
= 2.0*102cm/s
e)
since the trignometric function is (kx -?t) , sothe wave propagates in th -x direction
f)
the maximum transverse speed is
umax =2?fym
= 2?(2.0Hz)(6.0cm)
= 75cm/s
g)
we have
y(3.5cm ,0.26s) = 6.0cmsin[0.020?(3.5) +4.0?(0.26)]
= -2.0cm