Calculating the derivatives of wave equations to determine the direction of travel.

The equation for a wave moving along a straight wire is: (1) y= 0.5 sin (6 x - 4t) To look at the motion of the crest, let y = ym= 0.5 m, thus obtaining an equation with only two variables, namely x and t. a. For y= 0.5, solve for x to get (2) x(t) then take a (partial) derivative of x(t) to get the rate of change of x which is the velocity of the wave. A separate wave on the same wire is: (3) y= 0.5 sin (6x + 4t) b. For y= 0.5, solve for x to get (4) x(t) then take a (partial) derivative of x(t) to get the rate of change of x which is the velocity of the wave. c. From parts a and b, state how you can tell whether a wave is moving toward +x or toward -x direction.

A Standing wave is the sum of two given waves on a wire. Write its equation.

A certain wave and its reflection simultaneously travel along a wire. The two waves are: y1= .15 sin (5x - 3 Pi t) and y2= .15 sin (5x + 3 Pi t). When they combine, they form a standing wave. PART a. Write the equation of the standing wave produced on the wire. PART b. Calculate the distance between two adjacent nodes on the wire. PART c. Calculate the amplitude of the SHM of a point which is .84 meters from a node. PART d. Calculate the maximum speed at an antinode.

Given the wave speed, and the graph y(t) at location x, of a traveling wave, write y(x,t) with numbers for the constants.

A wave travels along a wire at 5 m/sec toward +x. SEE ATTACHMENT #1 for a diagram showing y and t axis system with scale values. PART a. Using information shown on the diagram, write y(x,t) in terms of k and (omega), with numbers for the constants. PART b. When t= 3 sec, and at x= 7 m, find y. PART c. At location x= 2.8 m, when y= -4 m, find the time t. PART d. Find the maximum particle speed of points on the wire.

A standing wave is set up in a guitar string. Find the first harmonic frequency. Then for a new frequency find new string tension and length.

A guitar string is .64 m long and has a linear density of .0004 kg/m. The tension is set at 55 newtons. SEE ATTACHMENT #1 for the general form of the equation of standing waves. PART a. Find the frequency of the first harmonic, the fundamental note emitted. PART b. Find the tension force required for the string to emit a fundamental note, or first harmonic, of 350 cy/sec. PART c. With tension at 55 nt, you press a fret to shorten the length for which the fundamental is 350 cy/sec. Find the new length.

Centre of mass

The figure shows a symmetric trapezoidal plate with a base of '2L'. The height and the top are each of length 'L' and the plate is of uniform density. Find the centre of mass of the trapezoid. P.S i have not included figure as scanner not working assuming know what it should look like. A rectangle with two triangles stuck on each side with measurements as given.