Oceanographers measured the sound velocity in seawater at various depths under two differe… — ACT

Oceanographers measured the sound velocity in seawater at various depths under two different salinity levels ( $34\text{ ppt}$ and $36\text{ ppt}$ ). The results are recorded in Table 1 below:

Depth (m)	Sound Velocity at 34 ppt (m/s)	Sound Velocity at 36 ppt (m/s)
0	1,520	1,523
200	1,495	1,498
600	1,475	1,478
1,000	1,470	1,473
1,500	1,480	1,483
2,000	1,490	1,493

Statement: If the data in Table 1 were translated into a two-line graph plotting Sound Velocity (m/s) on the y-axis against Depth (m) on the x-axis, both curves would reach a minimum value at a depth of $1,000\text{ m}$ , and the curve representing $36\text{ ppt}$ salinity would be positioned strictly above the curve representing $34\text{ ppt}$ salinity across all measured depths.

Answer: Answer

Answer

The statement is True.

The statement accurately reflects the conversion of the tabular data into a line graph. In Table 1, both sound velocity columns drop to their lowest values (

1,470\text{ m/s}

and

1,473\text{ m/s}

) at a depth of

1,000\text{ m}

before rising again, creating a V-shaped curve minimum at

x = 1,000\text{ m}

. Additionally, at every listed depth, the value for

36\text{ ppt}

is higher than for

34\text{ ppt}

, placing the

36\text{ ppt}

curve vertically above the

34\text{ ppt}

curve.

Step-by-Step Solution

Analyze the trend along the vertical axis variable (Sound Velocity) as a function of the horizontal axis variable (Depth) for both datasets.

For

34\text{ ppt}

, velocities are

1,520 \rightarrow 1,495 \rightarrow 1,475 \rightarrow 1,470 \rightarrow 1,480 \rightarrow 1,490

. The lowest point (minimum) occurs at

1,000\text{ m}

(

1,470\text{ m/s}

). For

36\text{ ppt}

, velocities are

1,523 \rightarrow 1,498 \rightarrow 1,478 \rightarrow 1,473 \rightarrow 1,483 \rightarrow 1,493

. The lowest point also occurs at

1,000\text{ m}

(

1,473\text{ m/s}

Determining where the graph reaches its lowest point requires identifying the minimum y-value for each x-value series.

Compare the relative vertical height (y-values) of the two salinity series across all depth levels (x-values).

At depth

0\text{ m}

1,523 > 1,520

; at

200\text{ m}

1,498 > 1,495

; at

600\text{ m}

1,478 > 1,475

; at

1,000\text{ m}

1,473 > 1,470

; at

1,500\text{ m}

1,483 > 1,480

; at

2,000\text{ m}

1,493 > 1,490

A curve with higher y-values at every x-value will be graphed higher up (above) another curve.

Synthesize the graphical behavior described in the statement with the tabular evidence.

Both curves reach a minimum at

1,000\text{ m}

and the

36\text{ ppt}

line remains strictly higher on the y-axis than the

34\text{ ppt}

line at all points. Thus, the statement is true.

The textual description of the proposed graph matches the tabular data perfectly in both shape (minimum location) and relative alignment.

Key Concept

Translating tabular data to graphical trends by matching values to axes, extrema, and relative curve placements.

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