Q-6. A 100 g wire is held under a tension of 250 N with one end at x = 0 and the other at x = 10.0 m. At time t = 0, pulse 1 is sent along the wire from the end at x = 10.0 m. At time t= 30.0 ms, pulse 2 is sent along the wire from the end at x = 0. At what position x do the pulses begin to meet?
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- A transverse wave has a frequency of ν = 74 Hz and a wavelength of λ = 11.5 m. The wave obtains a maximum displacement of ym = 2.5 m and propagates in the -x direction. Given the form y(x,t) = A sin(B) for the displacement of the wave, input an expression for A. Using the same form y(x,t) input an expression for B. How fast is the wave traveling in m/s?The wave function that models a standing wave is given as yR (x, t) = 6.00 cm sin (3.00 m−1 x + 1.20 rad) cos (6.00 s−1 t + 1.20 rad). What are two wave functions that interfere to form this wave function? Plot the two wave functions and the sum of the sum of the two wave functions at t = 1.00 s to verify your answer.s(x, t = 0.005s) s(x, t = 0s) y(mm)4 3 2 1 0 -1 -2 -3+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 x(m) = = 42. Consider the graph in the preceding problem of a compression wave. Shown are snapshots of the wave function for t 0.000 s (blue) and t 0.005s (orange). Given that the displacement of the molecule at time t 0.00 s and position x 0.00 m is = - s (0.00 m, 0.00 s) = 1.08 mm, derive a wave function to model the compression wave.
- A rope of length L = 5.2 m with a total mass of m = 0.275 kg is tied to a hook rigidly mounted into a wall. A pulse of height 1.9 cm is sent down the rope. The tension in the rope is F = 29 N. (B) What is the height of the pulse that returns?The power versus time for a point on a string (μ = 0.05 kg/m) in which a sinusoidal traveling wave is induced is shown in the preceding figure. The wave is modeled with the wave equation y(x, t) = A sin(20.93 m−1 x − ωt). What is the frequency and amplitude of the wave?Your answer is partially correct. A transverse wave on a string has an amplitude of 0.188 m and a frequency of 215 Hz. Consider the particle of the string at x = 0 m. It begins with a displacement of y=0m when t = 0 s. How much time passes between the first two instants when this particle has a displacement of y = 0.0817 m? Number i -0.000332 Units S
- We used an experimental setup like the one shown below. The length of the string between the string vibrator and the pulley is L = 2.00 m. The mass per unit length or linear density of the string is μ = 0.0005 kg/m. The string vibrator can oscillate at any frequency. The hanging mass is 511 g. Frictionless pulley String vibrator μl= dm dx The wavelength of the fifth mode (n = 5) is m. The frequency of the fifth mode (n = 5) is Hz. The tension in the string is close to When the mode of vibration is increased to n = 10, the wave speed of the string will → 2 The wave speed on the string is m/s. N. constant Drag answer here Drag answer here Drag answer here Drag answer here Drag answer here m Hanging mass 500 125 remain the same 0.8 100 2.0 increaseIt's Christmas time and you blast your Christmas music with the windows down in your car. Your grinchy roommate hears your music 30 meters away. The final note in the song is a B, playing at 493 Hz, but your roommate smiles because to him it sounds like a B-flat, playing at 440 Hz. How fast are you driving relative to your roommate? And in what direction?Problem 1 Let y1 = A sin(kr – wt + a) and y2 = B sin(kx – wt + B) be the equa- tions representing two traveling transverse wave. Here A and B are two possibly different amplitudes, and a and ß are two possibly different phase shifts. The wave vector k and angular frequency w of each wave are the same. a) What are the phasors for each wave, denoted 1 and 2? b) What is the sum of the phasors? c) What is the radius R and phase angle o of the phasor in part b)?
- Consider a monochromatic green lightwave with wavelength λ = 550 nm (1 nm = 1 * 10-9m). Assuming the speed of light in vacuum (which is close to the one in air) to be c = 3 * 108m/s, then: A. Calculate the period τ and the optical frequency v for green light? B. Write a sinusoidal harmonic wave with unit amplitude propagating towards the negative x-axis. Consider that for x = 0 and t = 0, the (initial) phase is (π/2). C. Plot the wave profile against x for following times: t = 0, 0.25τ, 0.5τ, and 0.75τ. Assume an arbitrary unit for the y-axis.Chapter 35, Problem 029 Two waves of the same frequency have amplitudes 0.843 and 2.41. They interfere at a point where their phase difference is 79.0°. What is the resultant amplitude? Number Units Use correct number of significant digits; the tolerance is +/-2%The figure below shows wave fronts of sound waves from the siren of a police car. Two people on both side of the car are running at 5 m/s to the left. The frequency of the siren is 400 Hz. The person on the left observes a frequency of 388.7 Hz. Speed of sound in air is 340 m/s. a) How fast is the policy car travelling? b) What is the frequency observed by the person on the right? c) What is the wavelength observed by the person on the righ? R