Question

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 this point.

c)Calculate the maximum transverse velocity of the string at this point.

d)Calculate the maximum transverse acceleration of the string at this point.

Answer #1

The following two waves are sent in opposite directions on a
horizontal string so as to create a standing wave in a vertical
plane:
y1(x, t) = (6.80 mm)
sin(4.80πx - 460πt)
y2(x, t) = (6.80 mm)
sin(4.80πx + 460πt),
with x in meters and t in seconds. An antinode is
located at point A. In the time interval that point takes
to move from maximum upward displacement to maximum downward
displacement, how far does each wave move along the...

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...

The second harmonic standing wave on a particular string fixed
at both ends is given by:
y(x, t) = 0.01 sin(2π x) cos(200π t)
(in SI units).
a) Fill in the following information:
λ2 = f2 = v =
b) How long is the string, and what is its fundamental
frequency?
L = f1 =
c) This second harmonic wave has total energy E2. If the string
is plucked so that has the first harmonic wave on it instead at...

A guitar string vibrates in its fundamental mode, with nodes at
its ends. The length of the rope segment that vibrates freely is
0.386 m. The maximum transverse acceleration of a point at the
midpoint of the segment is 8.40x103 m / s2, and the maximum
transverse velocity is 3.80 m / s. a) Calculate the amplitude of
this standing wave. b) How fast are transverse traveling waves in
this rope?
a
a) 1.72 m
b) 543 m/s
b
a)...

Oscillation of a 230 Hz tuning fork sets up standing waves in a
string clamped at both ends. The wave speed for the string is 750
m/s. The standing wave has four loops and an amplitude of 1.6 mm.
(a) What is the length of the string? (b) Write an equation for the
displacement of the string as a function of position and time.
Round numeric coefficients to three significant digits.

A standing wave is set up in a L=2.00m long string fixed at both
ends. The string vibrates in its 5th harmonic when driven by a
frequency f=120Hz source. The mass of the string is m=3.5grams.
Recall that 1kg = 1000grams.
A. Find the linear mass density of the string
B. What is the wavelength of the standing wave
C. What is the wave speed
D. What is the tension in the string
E. what is the first harmonic frequency...

Two waves traveling on a string in the same direction both have
a frequency of 100 Hz, a wavelength of 2 cm, and an amplitude of
0.02 m. What is the amplitude of the resultant wave if the original
waves differ in phase by each of the following values?
(a) π/6 cm
(b) π/3

1a. Derive a formula for the wavelength of a standing wave on a
fixed string at both ends in terms of the number of antinodes, n,
and the length of the string.
1b. For an aluminum rod, when a wave is set up in the rod, do
you expect the ends of the rod to allow vibrations or not? Are they
considered open or closed for displacement?
1c. Draw schematic pictures of the two longest wavelengths that
could fit on...

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)....

Transverse waves traveling along a string have the following
properties.
Amplitude of the wave = 2.30 mm
Wavelength of the wave = 0.128 m
Speed of the wave = 328 m/s
a) Determine the time for a particle of the string to move
through a total distance of 1.50 km. in s
b) If the string is held under a tension of 982 N, determine its
linear density. in g/m

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