A wave on a string is described by the following equation (assume the +x direction is...
A wave on a string is described by the following equation (assume the +x direction is to the right).
y = (12 cm) cos[πx/(4.0 cm) + π t/(19 s)]
(a) What is the amplitude of this wave?
(b) What is its wavelength?
(c) What is its period?
(d) What is its speed?
cm/s (e) In which direction does the wave travel?
Homework Answers
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A wave on a string is described by the following equation
(assume the +x direction is...
A sinusoidal transverse wave is travelling along a string in the negative direction of an x...
A sinusoidal transverse wave is travelling along a string in the negative direction of an x axis. The figure shows a plot of the displacement as a function of position at time t = 0; the y intercept is 4.0 cm. The string tension is 3.3 N, and its linear density is 44 g/m. Find the (a) amplitude, (b) wavelength, (c) wave speed, and (d) period of the wave, (e) Find the maximum transverse speed of a particle in the...
A transverse wave is given by the following equation: y (x,t) = (2.45 cm) cos [(0.420...
A transverse wave is given by the following equation: y (x,t) = (2.45 cm) cos [(0.420 rad/cm)x + (5.20 rad/s)t] a) What are the wave's amplitude, frequency, period, and wavelength? b) What is the direction of wave travel, and what is the speed? c) What is the displacement of a particle at x = 5.00 m, at t = 1.00 min? Hint: pay attention to units!
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...
A string oscillates according to the equation y´ = (0.754 cm) sin[(π/4.0 cm-1)x] cos[(36.7 π s-1)t]....
A string oscillates according to the equation y´ = (0.754 cm) sin[(π/4.0 cm-1)x] cos[(36.7 π s-1)t]. What are the (a) amplitude and (b) speed of the two waves (identical except for direction of travel) whose superposition gives this oscillation? (c) What is the distance between nodes? (d) What is the transverse speed of a particle of the string at the position x = 1.05 cm when t = 1.12 s? I have everything except part (d) the units for it...
Question: A standing wave is established in a string and can be described by the equation:...
Question: A standing wave is established in a string and can be described by the equation: y(2, t) = 4.18 sin(14.4x) cos(980t) cm. Where z is in m and t is in s. Part 1) What is the position of the first anti-node? m Part 2) What is the maximum speed of a piece of string at x = 0.309 m? Umax = m/s Part 3) This standing wave is formed from an input wave travelling to the right interfering...
A traveling wave is described by the equation: TT y(x, t) = (0.35 cm) sin (...
A traveling wave is described by the equation: TT y(x, t) = (0.35 cm) sin ( 3173 107t + 4 Find: a. the wavelength of the wave; b. the period of the wave; c. the speed and direction of travel of the wave; Now consider the particle at x = 10 cm. d. Find the vertical displacement of the particle t = 0. e. Find the maximum transverse speed and acceleration of the particle. If the oscillator that is generating...
SELF TESTI 1. A wave is described by the equation y = 4 sin(31-6x) (SI units)....
SELF TESTI 1. A wave is described by the equation y = 4 sin(31-6x) (SI units). a) Is the wave traveling in the +x or -x direction? b) Determine the amplitude, angular frequency, wavenumber, frequency, period, and wavelength (don't forget units). 2. A wave moves along a string in the +x direction with a speed of 8.0 m/s, a frequency of 4.0 Hz, and amplitude of 0.050 m. a) Determine the wavelength. b) Determine the wavenumber. c) Determine the period....
A wave traveling in a string in the positive x direction has a wavelength of 35...
A wave traveling in a string in the positive x direction has a wavelength of 35 cm, an amplitude of 8.4 cm, and a period of 1.2 s. What is the wave equation (in base SI units) that correctly describes this wave? y(x,t)=0.084 sin(18x+5.2t) y(x,t)=0.084 sin(18x−5.2t) y(x,t)=0.084 sin(0.35x+1.2t) y(x,t)=0.084 sin(0.35x−1.2t) y(x,t)=0.084 sin(2.9x−0.83t)
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...
A string oscillates according to the equation y´ = (0.529 cm) sin[(π/6.0 cm-1)x] cos[(42.4 π s-1)t]....
A string oscillates according to the equation y´ = (0.529 cm) sin[(π/6.0 cm-1)x] cos[(42.4 π s-1)t]. What are the (a) amplitude and (b) speed of the two waves (identical except for direction of travel) whose superposition gives this oscillation? (c) What is the distance between nodes? (d) What is the transverse speed of a particle of the string at the position x = 1.64 cm when t = 1.18 s?
A sinusoidal transverse wave is travelling along a string in the negative direction of an x axis. The figure shows a plot of the displacement as a function of position at time t = 0; the y intercept is 4.0 cm. The string tension is 3.3 N, and its linear density is 44 g/m. Find the (a) amplitude, (b) wavelength, (c) wave speed, and (d) period of the wave, (e) Find the maximum transverse speed of a particle in the...
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...
Question: A standing wave is established in a string and can be described by the equation: y(2, t) = 4.18 sin(14.4x) cos(980t) cm. Where z is in m and t is in s. Part 1) What is the position of the first anti-node? m Part 2) What is the maximum speed of a piece of string at x = 0.309 m? Umax = m/s Part 3) This standing wave is formed from an input wave travelling to the right interfering...
A traveling wave is described by the equation: TT y(x, t) = (0.35 cm) sin ( 3173 107t + 4 Find: a. the wavelength of the wave; b. the period of the wave; c. the speed and direction of travel of the wave; Now consider the particle at x = 10 cm. d. Find the vertical displacement of the particle t = 0. e. Find the maximum transverse speed and acceleration of the particle. If the oscillator that is generating...
SELF TESTI 1. A wave is described by the equation y = 4 sin(31-6x) (SI units). a) Is the wave traveling in the +x or -x direction? b) Determine the amplitude, angular frequency, wavenumber, frequency, period, and wavelength (don't forget units). 2. A wave moves along a string in the +x direction with a speed of 8.0 m/s, a frequency of 4.0 Hz, and amplitude of 0.050 m. a) Determine the wavelength. b) Determine the wavenumber. c) Determine the period....
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...
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