Question

A guitar string lies along the x-axis when in equilibrium. The end of the string at x = 0 is fixed. A sinusoidal wave with amplitude 0.75mm and frequency 440Hz, travels along the string in x-direction at 143m/s. It is reflected from the fixed end, and the superposition of the incident and reflected waves forms a standing wave.

(a) Find the equation giving the displacement of a point on the string as a function of position and time.

(b) Locate the nodes and antinodes.

Answer #1

A wave propagates along a string and is reflected at the free
end of the string. If we set the free end of the string as x=0, the
wave can be described by y=0.2sin(1.5*pi*x-pi*t); here y is in unit
of meters, and t is in unit of seconds.
(a) What is the resultant wave equation when the reflected wave
combines with the incoming wave?
(b) What would be the resultant wave equation if the end of
string (x=0) is not...

A string with linear density 1.70 g/m is stretched along the
positive x-axis with tension 18.0 N. One end of the string, at x =
0.00 m, is tied to a hook that oscillates up and down at a
frequency of 177.0Hz with a maximum displacement of 0.695 mm. At t
= 0.00 s, the hook is at its lowest point.
What is the wave speed on the string
What is the wavelength?

A transverse sinusoidal wave is moving along a string in the
positive direction of an x axis with a speed of 93 m/s. At t = 0,
the string particle at x = 0 has a transverse displacement of 4.0
cm from its equilibrium position and is not moving. The maximum
transverse speed of the string particle at x = 0 is 16 m/s. (a)
What is the frequency of the wave? (b) What is the wavelength of
the wave?...

A wave travels along a taut string in the positive x-axis
direction. Its wavelength is 40 cm and its speed of propagation
through the string is 80 m / s. The amplitude of the wave is 0.60
cm. At t = 0 the point of the chord at x = 0 is at the point of
maximum oscillation amplitude, y = + A.
a) Write the equation of the wave in the form of sine [y = A sin
(kx...

A wave travels along a taut string in the positive x-axis
direction. Its wavelength is 40 cm and its speed of propagation
through the string is 80 m / s. The amplitude of the wave is 0.60
cm. At t = 0 the point of the chord at x = 0 is at the point of
maximum oscillation amplitude, y = + A.
a) Write the equation of the wave in the form of sine [y = A sin
(kx...

Simple harmonic wave, with phase velocity of 141ms^-1, propagates
in the positive x-direction along a taut string that has a linear
mass density of 5gm^-1. The maximum amplitude of the wave is 5cm
and the wavelength is 75cm.
a) determine the frequency of the wave
b) write the wave function down the amplitude at time t = 0
and x = 0 is 2.5 cm.
c) calculate the maximum magnitude of the transverse velocity
(of a particle on the string)....

A string with both ends held fixed is vibrating in its third
harmonic. The waves have a speed of 193 m/s and a frequency of 235
Hz. The amplitude of the standing wave at an antinode is 0.380
cm.
a)Calculate the amplitude at point on the string a distance of
16.0 cm from the left-hand end of the string.
b)How much time does it take the string to go from its largest
upward displacement to its largest downward displacement at...

A 4.70-m-long string that is fixed at one end and attached to a
long string of negligible mass at the other end is vibrating in its
fifth harmonic, which has a frequency of 428 Hz. The amplitude of
the motion at each antinode is 2.82 cm.
(a) What is the wavelength of this wave?
?5 = m
(b) What is the wave number?
k5 = m?1
(c) What is the angular frequency?
?5 = s?1
(d) Write the wave function for this standing...

Four waves are to be sent along the same string, in the same
direction y1(x,t) = (2 mm) sin(2px – 200pt)
y2(x,t) = (2 mm) sin(2px – 200pt + 0.7p) y3(x,t) = (2 mm)
sin(2px – 200pt + p) y4(x,t) = (2 mm) sin(2px – 200pt + 3.7p)
(a) For y1, what is the (a) frequency, (b) wavelength and (c)
speed? When these waves are all added together, what is the (d)
amplitude of the resultant wave?

A thin, non conducting rod with length L lies along the positive
X-Axis with one end at the origin. The rod carries a charge
distributed along its length of λ(x) = bx/L. Determine the electric
potential along the X-Axis at the point x = 2 cm if L = 1 cm and b
= 50 pC/m. Answer = (0.17 V)

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