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Four waves are described by the following equations; where distances are measured in meters and times in seconds. y = 0.12 cos(3x- 21t) y = 0.15 sin(6x + 42t) Y=0.13 cos(6x + 210 IVy =-0.23 sin(3x - 42t) Which of these waves have the same period? and Ill, and also Il and IV and Il, and also IIl and IV and IV, and also and All of them have the same period They all have different periods

Respuesta :

The correct option is A) I and III, and also II and IV.

The equation of wave is given by;

y = Asin(kx - ωt)

         or

y = Acos(kx - ωt)

(depending or the waveform)

where;

A is the amplitude of the wave in meters

y(x,t) is the displacement in meters

k = 2π/λ is the propagation constant

ω = 2π/T is the angular frequency in radian per seconds

T = 2π/ω;

T is the time period in seconds

+ve and -ve signs show the direction of the wave.

I) Comparing y = 0.12cos(3x - 21t) with the general equation;

          ωt = 21t

          ω = 21

      2π/T = 21

          T = 2π/21 seconds

II) Comparing y = 0.15 sin(6x + 42t)  with the general equation;

        ωt = 42t

        ω = 42

   2π/T = 42

        T = 2π/42 seconds

III) Comparing y = 0.13 cos(6x + 21t) with the general equation;

        ωt = 21t

        ω = 21

   2π/T = 21

         T = 2π/21 seconds

IV) Comparing y = -0.23 sin(3x - 42t) with the general equation;

        ωt = 42t

        ω = 42

   2π/T = 42

         T = 2π/42 seconds    

Therefore I and III have the same period, II and IV have the same period.

To know more about waves visit:

https://brainly.com/question/13843093

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