3. A long string is tensioned to F = 80 N. A pulse traveling along the string has the following wave function, y(x,t) A 1+ 3(x = vt)² Find an expression for the total energy per unit length of string. Integrate this over the entire string to find the total energy of the pulse. Compute the total energy of the pulse when A = 0.010 m and ẞ= 0.25 m2. (Answer 3.1 mJ). 3. A long string is tensioned to F = 80 N. A pulse traveling along the string has the following wave function, y(x,t) A 1+ 3(x = vt)² Find an expression for the total energy per unit length of string. Integrate this over the entire string to find the total energy of the pulse. Compute the total energy of the pulse when A = 0.010 m and ẞ= 0.25 m2. (Answer 3.1 mJ).

A harmonic transverse wave function is given by y(x, t) = (0.850 m) sin (15.3x + 10.4t) where all values are in the appropriate SI units. a. What are the propagation speed and direction of the waves travel? b. What are the waves period and wavelength? c. What is the amplitude? d. If the amplitude is doubled, what happens to the speed of the wave?

Two sinusoidal waves are moving through a medium in the same direction, both having amplitudes of 3.00 cm, a wavelength of 5.20 m, and a period of 6.52 s, but one has a phase shift of an angle . What is the phase shift if the resultant wave has an amplitude of 5.00 cm? [Hint: Use the trig identity sinu+sinv=2sin(u+v2)cos(uv2)

A standing wave on a string is described by the equation y(x, t) = 1.25 sin(0.0350x) cos(1450t), where x is in centimeters, t is in seconds, and the resulting amplitude is in millimeters. a. What is the length of the string if this standing wave represents the first harmonic vibration of the string? b. What is the speed of the wave on this string?

A wave is described by y = 0.020 0 sin (kx - t), where k = 2.11 rad/m, = 3.62 rad/s, x and y are in meters, and t is in seconds. Determine (a) (he amplitude, (b) the wavelength, (c) the frequency, and (d) the speed of the wave.

Let us assume we are using SI units (kg, m, s). Consider the harmonic travelling wave 17 y(x, t) = = 12 cos(3x - 12πt). Assume the above harmonic wave is a solution of the motion of a string with tension T = 1 Newton. What is the string's density?p= kg/m What is its kinetic energy density? What is its kinetic energy over one wavelength? Ek What is its potential energy density? What is its potential energy over one wavelength? Ey = J/m J/m

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5T Consider a wave described by the wave function y (x,t) = 0.50m sin (I -1 -1 х + t + ), find the frequency of wave? 4 10 a. 1.2 Hz O b. 1.35 Hz C. 1.125 Hz Od. 0.89 Hz

A wave is modeled by the wave function: y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)] 1. Find the wavelength, wave number, wave velocity, period and wave frequency. 2. Construct on the computer, in the same graph, the dependence of y (x, t) from x on t = 0 and t = 5 s and the amplitude is A= 1.3m 3. After constructing the graph, make the appropriate interpretations and comments from the result that you got graphically. 4. How much is the wave displaced during the time interval from t = 0 to t = 5 s? Does it match this with the graph results? Justify your answer. Is the material transported long wave displacement? If yes, how much material is transported over time interval from t = 0 to t = 5 s? Comment on your answer. We now consider two sound waves with different frequencies which have to the same amplitude. The wave functions of these waves are as follows: y1 (t) = A sin (2πf1t) y2 (t) = A sin (2πf2t) 5. Find the resultant wave function analytically. 6. Study how the resulting wave…

A sinusoidall wave traveling in the positive x direction has an amplitude of 30.0 cm, a wavelength of 80.0 cm, and a frequency of 18.0 Hz. Find the angular frequency. O 103.5010 Hz O 100.5310 Gz O 100.5310 Hz O 105.3010 Hz