The equation of a transverse wave traveling along a very long string is y = 6.0 sin(0.020πx + 4.0πt), where x and y are expressed in centimeters and t is in seconds. Determine (a) the amplitude, (b) the wavelength, (c) the frequency, (d) the speed, (e) the direction of propagation of the wave, and (f) the maximum transverse speed of a particle in the string. (g) What is the transverse displacement at x = 3.5 cm when t = 0.26 s?

a) A = 6.0 cm , b)  λ = 100 cm , c)  f = 0.5 Hz, d) v = 0.5 m / s, e)  the wave propagates to the right , f)  v = 0.12π m / s, g)   y = -1.67 cm

Explanation:

The general equation of a wave on a string going off to the right is

          y = A sin (kx - wt)

where A is the amplitude of the movement. w the angular velocity and k the wave number

in this exercise the equation remain is

        y = 6.0 sim (0.020π x - 4.0π t)

a) Let's compare the two equations to find the answers

       the amplitude is

         A = 6.0 cm

b) The wave number is

         k = 2π/λ

         λ = 2π / k

         λ = 2π / 0.020π

         λ = 100 cm

c) angular velocity is related to frequency

          w = 2π f

          f = 2π / w

          f = 2π / 4.0π

          f = 0.5 Hz

d) at wave speed is given by

          v = λ f

          v = 1   0.5

          v = 0.5 m / s

e) as the temporal part is negative, the wave propagates to the right

f) we find the maximum transverse speed from the equation

       v = dy / dt

       v = -A w cos kx-wt)

the speed is maximum when the cosine function is ±1

        v = -A w

         v = 6.0  0.020π

         v = 0.12π m / s

g) the displacement for x = 3.5 cm t = 0.26 s

          y = 6.0 sin (0.020π 6.5 - 4.0π 0.26)

          y = 6.0 (-0.279)

          y = -1.67 cm

freezing

deposition

condensation

explanation;

melting also called fusion is the process where solid becomes liquid, sublimation is the process where solid becomes gaseous without first changing to liquid, deposition involves change from gaseous to solid state, freezing involves change from liquid to solid, boiling or evaporation involves change of liquid to gaseous state, while condensation is the change from gaseous state to liquid state.

endothermic reactions involves absorption of heat from the surroundings or the environment while exothermic reactions involves loss of heat energy to the surroundings.

in this case, sublimation, evaporation and melting are endothermic reactions (gain energy from the environment) while, freezing, deposition and condensation are exothermic (loss of energy to the surroundings) reactions.

answer: option c.

explanation: