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The displacement of a string of tension 20 N is given by: y(x,t)=0.04sin(270x - 607). Determine:...
The vertical displacement y(x,t) of a string stretched along the horizontal x-axis is given by y(x,t)...
The vertical displacement y(x,t) of a string stretched along the horizontal x-axis is given by y(x,t) = (6.00 mm) sin[(3.25 rad/m) x - (7.22 rad/s)t]. First, determine the constant speed of this wave. Next, calculate the instantaneous speed of a particle of the string located at x = 1.25 m at the time of 10.00 s. Finally take the constant speed of the wave and divide by the instantaneous speed of the particle that you determined. Watch your units -...
The equation of a transverse wave traveling along a very long string is given by y...
The equation of a transverse wave traveling along a very long string is given by y = 6.1 sin(0.018πx + 3.1πt), where x and y are expressed in centimeters and t is in seconds. Determine the following values. (a) the amplitude cm (b) the wavelength cm (c) the frequency Hz (d) the speed cm/s (e) the direction of propagation of the wave +x−x +y−y (f) the maximum transverse speed of a particle in the string cm/s (g) the transverse displacement at...
3. The vertical displacement of a string is given by the harmonic function: Y(x, t) =...
3. The vertical displacement of a string is given by the harmonic function: Y(x, t) = 3.5cos(12nt-187x) Where x is the horizontal distance along the string in meters. Suppose a tiny particle were attached to the string at x=5cm. obtain the expression for the vertical velocity of the particle as a function of time.
A sinusoidal transverse wave is traveling along a string in the negative direction of an x...
A sinusoidal transverse wave is traveling along a string in the
negative direction of an x axis. The figure below shows a
plot of the displacement as a function of position at time
t = 0. The x axis is marked in increments of 10
cm and the y axis is marked in increments of 2 cm. The
string tension is 3.1 N, and its linear density is 34 g/m.
(a) Find the amplitude.
m
(b) Find the wavelength.
m...
To practice Problem-Solving Strategy 15.1 Mechanical Waves. Waves on a string are described by the following...
To practice Problem-Solving
Strategy 15.1 Mechanical Waves. Waves on a string are described by
the following general equation y(x,t)=Acos(kx−ωt). A transverse
wave on a string is traveling in the +x direction with a wave speed
of 7.50 m/s , an amplitude of 9.00×10−2 m , and a wavelength of
0.550 m . At time t=0, the x=0 end of the string has its maximum
upward displacement. Find the transverse displacement y of a
particle at x = 1.40 m and...
The wave function for a standing wave on a string is described by y(x, t) =...
The wave function for a standing wave on a string is described by y(x, t) = 0.016 sin(4πx) cos (57πt), where y and x are in meters and t is in seconds. Determine the maximum displacement and maximum speed of a point on the string at the following positions. (a) x = 0.10 m ymax = m vmax = m/s (b) x = 0.25 m ymax = m vmax = m/s (c) x = 0.30 m ymax = m vmax = m/s (d) x = 0.50...
The equation of a transverse wave traveling along a very long string is y = 3.96...
The equation of a transverse wave traveling along a very long string is y = 3.96 sin(0.0444πx+ 7.89πt), where x and y are expressed in centimeters and t is in seconds. Determine (a) the amplitude, (b) the wavelength, (c) the frequency, (d) the speed, (e) the direction of propagation of the wave and (f) the maximum transverse speed of a particle in the string. (g) What is the transverse displacement at x = 1.05 cm when t = 0.843 s?
A wave on a string is described by y(x,t)=( 2.0 cm )×cos[2π(x/( 3.6 m )+t/( 0.20...
A wave on a string is described by y(x,t)=( 2.0 cm )×cos[2π(x/( 3.6 m )+t/( 0.20 s ))] , where x is in m and t is in s. A)In what direction is this wave traveling? Negative B)What is the wave speed? 18 m/s C)What is the wave frequency? Hz D)What is the wave length? m E)At t = 0.50 s , what is the displacement of the string at x = 0.30 m ? cm
The displacement of a transverse traveling wave on a string under tension is described by: D(x,...
The displacement of a transverse traveling wave on a string under tension is described by: D(x, t) = (2.0 cm) .sin((12.57 rad/m)x + (638 rad/s)t + /2] The linear density of the string is 5.00 g/m. 1. What is the tension in the string? 2. What is the maximal speed of a point on the string? String 2 3. The original string (String 1) is tied to a second string with String 1 a linear density of 12 g/m, as...
The displacement of a transverse traveling wave on a string under tension is described by: D(x,...
The displacement of a transverse traveling wave on a string under tension is described by: D(x, t) = (2.0 cm) sin((12.57 rad/m)x+ (638 rad/s)t + T/2] The linear density of the string is 5.00 g/m. 1. What is the tension in the string? 2. What is the maximal speed of a point on the string? String 2 3. The original string (String 1) is tied to a second string with String 1 a linear density of 12 g/m, as shown...
The vertical displacement y(x,t) of a string stretched along the horizontal x-axis is given by y(x,t) = (6.00 mm) sin[(3.25 rad/m) x - (7.22 rad/s)t]. First, determine the constant speed of this wave. Next, calculate the instantaneous speed of a particle of the string located at x = 1.25 m at the time of 10.00 s. Finally take the constant speed of the wave and divide by the instantaneous speed of the particle that you determined. Watch your units -...
3. The vertical displacement of a string is given by the harmonic function: Y(x, t) = 3.5cos(12nt-187x) Where x is the horizontal distance along the string in meters. Suppose a tiny particle were attached to the string at x=5cm. obtain the expression for the vertical velocity of the particle as a function of time.
A sinusoidal transverse wave is traveling along a string in the
negative direction of an x axis. The figure below shows a
plot of the displacement as a function of position at time
t = 0. The x axis is marked in increments of 10
cm and the y axis is marked in increments of 2 cm. The
string tension is 3.1 N, and its linear density is 34 g/m.
(a) Find the amplitude.
m
(b) Find the wavelength.
m...
To practice Problem-Solving
Strategy 15.1 Mechanical Waves. Waves on a string are described by
the following general equation y(x,t)=Acos(kx−ωt). A transverse
wave on a string is traveling in the +x direction with a wave speed
of 7.50 m/s , an amplitude of 9.00×10−2 m , and a wavelength of
0.550 m . At time t=0, the x=0 end of the string has its maximum
upward displacement. Find the transverse displacement y of a
particle at x = 1.40 m and...
The displacement of a transverse traveling wave on a string under tension is described by: D(x, t) = (2.0 cm) .sin((12.57 rad/m)x + (638 rad/s)t + /2] The linear density of the string is 5.00 g/m. 1. What is the tension in the string? 2. What is the maximal speed of a point on the string? String 2 3. The original string (String 1) is tied to a second string with String 1 a linear density of 12 g/m, as...
The displacement of a transverse traveling wave on a string under tension is described by: D(x, t) = (2.0 cm) sin((12.57 rad/m)x+ (638 rad/s)t + T/2] The linear density of the string is 5.00 g/m. 1. What is the tension in the string? 2. What is the maximal speed of a point on the string? String 2 3. The original string (String 1) is tied to a second string with String 1 a linear density of 12 g/m, as shown...
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