A snapshot graph at t=0 s for the displacement of a string is shown below. The wave is traveling to the left at 20 m/s. I forgot to label the horizontal axis, but it goes from 0 cm to 10 cm. D (cm) -5- 5 10 A. What is the equation for this wave function D(x,t)? B. What are the instantaneous speed and acceleration of the point of the string at x=5 m at t=0 s? (You need to use calculus here.)

A transverse wave on a string is described with the wave function y(x,t)=(0.50cm)sin(1.57m1x6.28s1t) . (a) What is the wave velocity of the wave? (b) What is the magnitude of the maximum velocity of the string perpendicular to the direction of the motion?

Consider two wave functions y1(x,t)=Asin(kxt) and y2(x,t)=Asin(kx+t+) . The resultant wave form when you add the two functions is yR=2Asin(kx+2)cos(t+2) . Consider the case where A=0.03m1,k=1.26m1,=s1 , and =10 . (a) Where are the first three nodes of the standing wave function starting at zero and moving in the positive x direction? (b) Using a spreadsheet, plot the two wave functions and the resulting function at time t=1.00 s to verify your answer.

A surface ocean wave has an amplitude of 0.60 m and the distance from trough to trough is 8.00 m. It moves at a constant wave speed of 1.50 m/s propagating in the positive x-direction. At t=0 , the water displacement at x=0 is zero, and vyis positive. (a) Assuming the wave can be modeled as a sine wave, write a wave function to model the wave. (b) Use a spreadsheet to plot the wave function at times t=0.00s and t=2.00s on the same graph. Verify that the wave moves 3.00 m in those 2.00 s.

Ocean waves with a crest-to-crest distance of 10.0 m can be described by the wave function y(x, t) = 0.800 sin [0.628(x - t)] where x and y are in meters, t is in seconds, and = 1.20 m/s. (a) Sketch y(x, t) at t = 0. (b) Sketch y(x, t) at t = 2.00 s. (c) Compare the graph in part (b) with that for part (a) and explain similarities and differences. (d) How has the wave moved between graph (a) and graph (b)?

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?

A string on the violin has a length of 23.00 cm and a mass of 0.900 grams. The tension in the string 850.00 N. The temperature in the room is TC=24.00C . The string is plucked and oscillates in the n=9 mode. (a) What is the speed of the wave on the string? (b) What is the wavelength of the sounding wave produced? (c) What is the frequency of the oscillating string? (d) What is the frequency of the sound produced? (e) What is the wavelength of the sound produced?

Consider the following wave function in SI units: P(r,t)=(25.0r)sin(1.36r2030t) Explain how this wave function can apply to a wave radiating from a small source, with r being the radial distance from the center of the source to any point outside the source. Give the most detailed description of the wave that you can. Include answers to such questions as the following and give representative values for any quantities that can be evaluated. (a) Does the wave move more toward the right or the left? (b) As it moves away from the source, what happens to its amplitude? (c) Its speed? (d) Its frequency? (e) Its wavelength? (f) Its power? (g) Its intensity?

A dog swims from one end of a pool to the opposite end. Is the dogs motion described as a wave? Explain.

A transverse wave on a string is modeled with the wave function y(x,t)=0.10msin(0.15m1x+1.50s1t+0.20) . (a) Find the wave velocity. (b) Find the position in the y-direction, the velocity perpendicular to the motion of the wave, and the acceleration perpendicular to the motion of the wave, of a small segment of the string centered at x=0.40 m at time t=5.00 s.