Consider a string of length 0.4 m which is fixed at both ends. It is initially stationery. The string is plucked, giving rise to an initial small displacement. (a) Obtain the appropriate wave equation that is satisfied by this string. (b) Obtain expressions for the displacement and velocity of the string. (c) Determine the frequencies of the different modes of the vibrating string.
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Q: mechanical waves, standing waves Begin Date: 6/29/2021 12:01:00 AM -- Due Date: 8/4/2021 11:59:00 PM…
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- A taut rope is tied to a machine that causes it to oscillate sinusoidally. You take a picture of the rope and see that at that moment there are four complete cycles along 10m. If the oscillator frequency is 20HZ, find: a) The wave number b) The angular frequency c) If at time t = Os, the height of the wave is Om when x = 0m, find the phase shift of the oscillation. d) If at time t = Os, the transverse velocity is 250m / s when x = Om, find the amplitude of the oscillation. e) Write the wave function that describes the behavior of this wave.you have a string with a mass of 0.0121 kg. you stretch the string with a force of 9.57 N, giving it a length of 1.95 m. then, you vibrate the string transversely at precisely the frequency that corresponds to its fourth normal mode; that is, at its fourth harmonic. what is the wavelength of the standing wave created in the string? what is the frequency?If a string were replaced with a less dense string while keeping node numbers and tension constant the same, what would happen to the required frequency to cause the standing wave?
- (d)v = 2/ghmax A wave traveling on a string has the following wave function, y(x, t) = Asin(kx + wt + p). At time 3D0, the point x = 0 has a displacement of y(0,0) = 0, and is moving in the negative y-direction. Which of the following is true about the phase constant and the wave speed direction? (a) o = "/2, and the wave is moving in the negative x-direction. (b) = "/2, and the wave is moving in the positive x -direction. 11) %3D (c) o = n and the wave is moving in the negative x -direction. (d)o = n and the wave is moving in the positive x -direction. 12) Two identical but separate strings, with the same tension, carry sinusoidal waves with the same frequency. Wave A has an amplitude that is twice that of wave B and transmits energy at a rate that is Lanswer below ) that ofwave B. (a) half (b)twice (c) one-fourth (d) four timesA string with a mass of 0.02 kg and a length of 2 meters is stretched between two fixed points. The tension in the string is 100 N. Calculate the speed of a transverse wave traveling through the string. (Note: Assume the string is massless, and there is no damping or energy loss during wave propagation.)A string is 1.5 m long and the wave travels at 250 m/s on the string. 1) What's the fundamental wavlength of the wave on a string? 2) What is the fudamental frequency? 3) What is the frequency of the fourth harmonic?
- Asinusoidal wave travels along a string. The time for a particular point to move from maximum displacement to zero is 0.15 s. What are the (a) period and (b) frequency? (c) The wavelength is 1.7 m; what is the wave speed? (a) Number i Units (b) Number Units (c) Number UnitsTwo waves that travel in opposite directions are superimposed on a rope. Both have the same period of oscillation and the same wavelength.(a) Consider the equations of these waves in the form y(x, t) = (0.05m)sin(πx/2 ± 12πt) in SI units and show that the sum of the two waves is a wave stationary.(b) If the resulting function represents the second harmonic in a string tensioned 200 N, determine the length of the string and its mass.A nylon string fixed at both ends vibrates with a fundamental frequency of 196 Hz. Which of the following would have a higher fundamental frequency than this string? An indentical string that is longer. A nylon string with twice the diameter, but the same length. An indentical string that is tightened to a higher tension. An identical string that is given a larger amplitude of vibration.
- A transverse periodic wave travels to the left along a string. Their characteristics are: amplitude of 0.200 m, wavelength of 0.350 m and a frequency of 12.0 Hz. The position of a portion of the string at t = 0, x = 0 is y = -0.0300 m, and the element has a positive velocity at that location. Find an expression for the wave function that describes it in terms of cosines.The wave function for a travelling wave on a taut string is: (SI units) y(x,t)=0.05 sin (4πx — 8πt) Deduce the general expressions for the transverse velocity and acceleration of a string element and their maximum values.Please Asap