Suppose a sinusoidal wave on a string, having amplitude A and travelling in the −xˆ direction,...

Suppose a sinusoidal wave on a string, having amplitude A and travelling in the −xˆ direction, is partially reflected at the point x = 0, so that the reflected wave is in phase with the incident wave at x = 0 but has amplitude kA, where 0 ≤ k ≤ 1 is the reflection coefficient. a) Show that each point on the string undergoes simple harmonic motion and determine how the amplitude of the simple harmonic motion varies with x b) Find the ratio of maximum to minimum amplitude, known as the standing wave ratio

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genius_generous answered 1 year ago

A transverse sinusoidal wave on a string is moving in the −x-direction. Its speed is 30.0...

A transverse sinusoidal wave on a string is moving in the −x-direction. Its speed is 30.0 m/s, and its period is 20.0 ms. At t = 0, a colored mark on the string at x = 0 has a vertical position of 2.00 cm and is moving down with a speed of 1.30 m/s. (a) What is the amplitude of the wave (in m)? 0.0204 Correct: Your answer is correct. m (b) What is the phase constant (in rad)? Incorrect:...

1. A sinusoidal voltage wave on a transmission line has real amplitude, V_0. The wave is...

1. A sinusoidal voltage wave on a transmission line has real amplitude, V_0. The wave is expressed in phasor form as V_s(z) = V_0*e^(-alpha*z)*e^(-j*(beta)*z) a. In which direction does this wave propagate and why? b. Express the given wave in real instantaneous form. c. The parameters of the line, operating at ω= 6.0×10^8 rad/s are L = 0.350 μH/m, C = 40.0 pF/m, G = 0 and R = 15.0 Ω/m. Find α,β,λ, andZ_0 (in magnitude and phase). d. Calculate...

A sinusoidal wave in a string is described by the wave function y = 0.155 sin...

A sinusoidal wave in a string is described by the wave function y = 0.155 sin (0.525x - 46.5t) where x and y are in meters and t is in seconds. The mass per length of the string is 13.2 g/m. (a) Find the maximum transverse acceleration of an element of this string. (b) Determine the maximum transverse force on a 1.00-cm segment of the string. (c) State how the force found in part (b) compares with the tension in...

A sinusoidal electromagnetic wave is propagating in a vacuum in the +z-direction. Part A If at...

A sinusoidal electromagnetic wave is propagating in a vacuum in the +z-direction. Part A If at a particular instant and at a certain point in space the electric field is in the +x-direction and has a magnitude of 3.40V/m , what is the magnitude of the magnetic field of the wave at this same point in space and instant in time? Part B What is the direction of the magnetic field?

A sinusoidal wave is traveling on a string with speed 34.9 cm/s. The displacement of the...

A sinusoidal wave is traveling on a string with speed 34.9 cm/s. The displacement of the particles of the string at x = 5.9 cm is found to vary with time according to the equation y = (3.9 cm) sin[1.2 - (7.1 s-1)t]. The linear density of the string is 4.8 g/cm. What are (a) the frequency and (b) the wavelength of the wave? If the wave equation is of the form y(x,t) = ym sin(kx - ωt), what are...

A transverse sinusoidal wave is generated at one end of a long, horizontal string by a...

A transverse sinusoidal wave is generated at one end of a long, horizontal string by a bar that moves up and down through a distance of 1.7 cm. The motion is continuous and is repeated regularly 160 times per second. The string has linear density 460 g/m and is kept under a tension of 140 N. Find the maximum value of (a) the transverse speed u and (b) the transverse component of the tension T. (c)Show that the two maximum...

Given two wave that has the same amplitude, frequency and direction that they are traveling in,...

Given two wave that has the same amplitude, frequency and direction that they are traveling in, BUT they have a phase that is a difference of 2Pi. When one adds both waves up we get: a) Nothing b) A wave with twice the wavelength of the original c) A wave with twice the amplitude of the original d) A wave with twice the frequency of the original e) None of the above

A transverse sinusoidal wave on a string has a period T = 27.0 ms and travels...

A transverse sinusoidal wave on a string has a period T = 27.0 ms and travels in the negative x direction with a speed of 30.0 m/s. At t = 0, a particle on the string at x = 0 has a transverse position of 2.00 cm and is traveling downward with a speed of 2.00 m/s. What is the phase constant? in rad Write the wave function for the wave. (Use the form Asin(kx + ωt + ϕ). Round...

A transverse sinusoidal wave on a string has a period T = 29.0 ms and travels...

A transverse sinusoidal wave on a string has a period T = 29.0 ms and travels in the negative x direction with a speed of 30.0 m/s. At t = 0, a particle on the string at x = 0 has a transverse position of 2.00 cm and is traveling downward with a speed of 1.50 m/s. (a) What is the amplitude of the wave? __________m (b) What is the phase constant? __________rad (c) What is the maximum transverse speed...

A transverse sinusoidal wave on a string has a period T = 33.0 ms and travels...

A transverse sinusoidal wave on a string has a period T = 33.0 ms and travels in the negative x direction with a speed of 30.0 m/s. At t = 0, a particle on the string at x = 0 has a transverse position of 2.00 cm and is traveling downward with a speed of 3.00 m/s. (a) What is the amplitude of the wave? m (b) What is the phase constant? rad (c) What is the maximum transverse speed...

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