Question

State the amplitude, period, midline and an equation involving the sine function for the graph shown below using a horizontal shift between ___ and ___.

Answer 1

• The given wave equation YR(x, t) = 0.35 cm sin (6.28 m¯¹x – 1.57 s¯¹t+) has an amplitude of 0.35 cm and a period of 1.57 s.
• The midline is y = 0.
• The equation involving the sine function is YR(x, t) = 0.35 cm sin (6.28 m¯¹x – 1.57 s¯¹t+).

Step-by-step explanation:

The given wave equation is YR(x, t) = 0.35 cm sin (6.28 m¯¹x – 1.57 s¯¹t+). To determine the amplitude, period, midline, and equation involving the sine function, we can analyze the given equation.

• Amplitude: The amplitude of a wave is the maximum displacement from the midline. In this case, the amplitude is 0.35 cm.
• Period: The period of a wave is the time it takes to complete one full cycle. The period can be found by looking at the coefficient in front of the variable 't'. In this case, the period is 1.57 s.
• Midline: The midline is the average height of the wave. Since the wave is a sine function, the midline is the horizontal line that the sine function oscillates around, which is y = 0.
• Equation: The equation involving the sine function is YR(x, t) = 0.35 cm sin (6.28 m¯¹x – 1.57 s¯¹t+).