Question

The equation of a transverse wave traveling along a string is y = 0.15 sin(0.79x - 13t), x and y are in meters and t is in seconds.

(a) What is the displacement y at x = 2.3 m, t = 0.16 s?

Answer 1

The displacement at
`\( x = 2.3 \, \text{m} \) and \( t = 0.16 \, \text{s} \) is \( y = 0.15 \sin(0.79 * 2.3 - 13 * 0.16) \).`

Step-by-step explanation:

The given equation
`\( y = 0.15 \sin(0.79x - 13t) \)`represents a transverse wave's displacement along a string.

To find the displacement at a specific point and time, substitute the given values into the equation. In this case, when
`\( x = 2.3 \, \text{m} \) and \( t = 0.16 \, \text{s} \),` the expression becomes
`\( y = 0.15 \sin(0.79 * 2.3 - 13 * 0.16) \).`

Breaking down the calculation, first evaluate the argument of the sine function:
`\( 0.79 * 2.3 - 13 * 0.16 \).` After obtaining this value, calculate the sine of the result and multiply it by 0.15.

The final result provides the displacement of the wave at the specified point and time.

This process is based on the general form of a transverse wave equation, where ( y ) represents displacement, ( x ) is the position along the wave, and ( t ) is the time.

The sine function captures the oscillatory behavior of the wave, and the coefficients determine the amplitude, wavelength, and speed. In this specific case, the values of ( x ) and ( t ) are substituted to find the displacement at a particular spatial and temporal location.