Question

tides in a specific location can be approximated using the periodic function shown on the graph. what is the interpretation of the amplitude in this application?

Explanation:

Step1: Recall Amplitude Definition

Amplitude of a periodic function (like a sinusoidal wave) is the maximum displacement from the midline (average value) to a peak (or trough). For a tide graph, the \( y \)-axis likely represents tide height (e.g., in meters or feet), and \( x \)-axis is time (e.g., hours).

Step2: Identify Midline and Peak/Trough

1. Find the midline: Average of maximum and minimum values. From the graph, max tide height (peak) is \( 2.4 \) (e.g., units), min (trough) is \( 0.5 \) (approx, looking at the lowest points around \( 0.4 - 0.6 \), let's use \( 0.5 \) for estimation). Midline \( = \frac{2.4 + 0.5}{2} \approx 1.45 \).
2. Amplitude is \( \text{Max} - \text{Midline} = 2.4 - 1.45 = 0.95 \) (or \( \text{Midline} - \text{Min} = 1.45 - 0.5 = 0.95 \)).

Step3: Interpret Amplitude in Context

Amplitude represents the maximum deviation of the tide height from its average (midline) height. So it's the maximum distance the tide rises above (or falls below) the average tide level at that location. For example, if average tide is ~1.45, the tide can rise \( \approx 1 \) unit (or whatever the \( y \)-axis units are) above average to a high tide, or fall \( \approx 1 \) unit below average to a low tide.

Answer:

The amplitude represents the maximum distance (in the units of the \( y \)-axis, e.g., height) that the tide level deviates from its average (midline) tide level. Specifically, it is the maximum amount the tide rises above (or falls below) the average tide height at this location.