Two sinusoidal waves in a string are defined by the wave functions Y1 = 2.10 sin (15.0x - 34.0t) Y22.10 sin (30.0x - 41.0t) where x, y₁, and y2 are in centimeters and t is in seconds. (a) What is the phase difference between these two waves at the point x = 5.00 cm at t = 2.00 s? (Your answer should be between 0° and 360°.) 255 (b) What is the positive x value closest to the origin for which the two phases differ by ± at t = 2.00 s? (At that location, the two waves add to zero.) 0.0304 x cm

A wave is represented by the equation y = (5.00 mm)sin [(5.00 mm¯¹) x − (8.00 s¯¹) t] + (2.00 mm) cos [(5.001 and t is in seconds. What is the amplitude of the wave? i mm n¯¹) x − (8.00 s¯¹) t], where y is in millimeters mm

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A progressive wave travelling in the x-direction is represented by the following equation: y = Asin(Bt - Cx). Given that parameters A, B and Care given in Sl units calculate the velocity of the wave for A = 50, B = 2694 and C = 21.

A wave has an equation of y(x,t) = (0.22 m) sin (503x-28.2t ) Assuming all parameters are in Sl units, calculate the frequency of the wave in Hz with two digits of precision.

Consider two sinusoidal waves: fi = A1 cos (kz – wt + ø1) and f2 = A2 cos (kz – wt + 02). We can write their complex forms as fi =Aje(kz-wt+61) = áeï(kz-wt) f2 =Aze(kz-wt+62) = Ãze³(kz-wt) where the complex amplitudes Ã1 = Ajeø1 and Ã, = Azeió2 Now suppose we want to combine the two: fs = fi + f2 = Ãze(k3:-w3t) = Azeiøs ei(kzz=wzt) Find expressions for A3, $3, k3, and w3.

Two waves on one string are described by the wave functions y​1​​= 3.33 cos(2.34x − 1.21t) y​2​​= 3.33 sin(4.37x − 2.57t) where x and y are in centimeters and t is in seconds. (Remember that the arguments of the trigonometric functions are in radians.) (a) Find the superposition of the waves y​1​​+y​2​​ at x = 1.0, t = 0.0 s.

A wave is described by the equation: with t in seconds and x in metres. (i) € (iv) y(x, t) = 0.6 sin[(2t - 6x) + +핑 Find the frequency, wavelength and wave number of this wave [Hint: write (2t-6x) as -(6x-2t) and then use trigonometric identities to interpret what y(x,t) = Asin[-(kx-ot)] represents graphically compared to y(x,t) = Asin(kx-cot). What is the propagation velocity/wave speed of this wave? What is the displacement and velocity of a particle at x = 0,3 m at t = 2 s? Based on your answer in (c) above, is the particle at x = 0,3 m moving away or towards the equilibrium at t = 2 s? Explain.