Question

The equation of a transverse wave traveling along a string is y=0.15sin(0.79x−13t), in which x and y are in meters and t is in seconds. What is the displacement y at x =2.3m, x=2.3 m,4t=0.16 s?

Answer 1

The displacement y of the transverse wave at position x = 2.3 m and time t = 0.16 s is approximately -0.039 meters, calculated by substituting values into the wave equation.

Step-by-step explanation:

To calculate the displacement y of a transverse wave on a string at a given position x and time t, we directly substitute these values into the wave equation y=0.15sin(0.79x−13t). Given that x = 2.3 m and t = 0.16 s, we substitute these values to get:

y = 0.15sin(0.79 × 2.3 − 13 × 0.16)

Carrying out the calculations:

y = 0.15sin(1.817 − 2.08)

y = 0.15sin(−0.263)

y ≈0.039 m

The displacement y at the given position and time is approximately −0.039 meters.