A wave is described by the equation y = (4.5×10−2) sin (1.9x − 3.2t), where lengths are measured in meters and time in seconds. What is the displacement of a particle at position x = 2.7 m at time t = 5.8 s? Note: Remember that the argument of the sine function in the wave equation is expressed in radians.

I don't have any idea

y = (4.5•10^−2) sin (1.9x − 3.2t) =

= (4.5•10^−2) sin (1.9•2.7 − 3.2•5.8)=
=(4.5•10^−2) sin (5.13 − 18.56)=
=(4.5•10^−2) sin (5.13 − 18.56)=
=(4.5•10^−2) •0.76 = - 0.034 m

To find the displacement of a particle at a specific position and time in a wave, we can use the given equation:

y = (4.5×10−2) sin (1.9x − 3.2t)

First, let's substitute the given values for x and t into the equation:

x = 2.7 m
t = 5.8 s

Now we can calculate the displacement:

y = (4.5×10−2) sin (1.9(2.7) − 3.2(5.8))

Simplifying the equation:

y = (4.5×10−2) sin (5.13 − 18.56)

y = (4.5×10−2) sin (-13.43)

Here, we need to convert the argument of the sine function to radians. Since the argument is already in radians, we can proceed with the calculation.

Using a calculator, find the sine of -13.43:

sin (-13.43) ≈ -0.244

Finally, multiply the result by (4.5×10−2):

y ≈ (4.5×10−2)(-0.244)

y ≈ -0.01098

Therefore, the displacement of the particle at position x = 2.7 m and time t = 5.8 s is approximately -0.01098 meters.

Note: The displacement is negative, indicating that the particle is displaced in the negative y-axis direction from the equilibrium position.