ACT Question

ACT Question for April 30th

Sound energy is transported through a medium by sound waves. The speed with which sound waves move through a medium is the speed of sound, V_s, for that medium.

This table gives V_s at 298 K for 3 metals having different d:

Are the data in the Table consistent with the hypothesis that as d for metals increases, V_s for metals increases only?

A) Yes, because the Table shows that V_s is greater when d equals 2.7 g/cm³ than when d equals 11.3 g/cm³, and that V_s is greater when d equals 11.3 g/cm³ than when d equals 19.3 g/cm³.

B) Yes, because the Table shows that V_s is greater when d equals 11.3 g/cm³ than when d equals 2.7 g/cm³, and that V_s is greater when d equals 19.3 g/cm³ than when d equals 11.3 g/cm³.

C) No, because the Table shows that V_s is greater when d equals 2.7 g/cm³ than when d equals 11.3 g/cm³.

D) No, because the Table shows that V_s is greater when d equals 11.3 g/cm³ than when d equals 19.3 g/cm³.

Correct

Incorrect

The correct answer is (C).

Getting to the Answer: Identify the relationship between d and V_s in the Table to determine if the data are consistent with the hypothesis that as d for metals increases, V_s increases only. According to the Table, as d increases from 2.7 to 11.3 to 19.3 g/cm³, V_s decreases from 6,400 to 2,000 and then increases to 3,200 m/sec. Therefore, the data are not consistent with the hypothesis. Eliminate (A) and (B), and then compare the statements in (C) and (D) to the Table to determine which matches the data.

(A) Incorrect: the data in the Table are not consistent with the hypothesis that as d increases, V_s increases only; also, V_s when d equals 11.3 g/cm³ is not greater than V_s when d equals 19.3 g/cm³

(B) Incorrect: the data in the Table are not consistent with the hypothesis that as d increases, V_s increases only; also, V_s when d equals 11.3 g/cm³ is not greater than V_s when d equals 2.7 g/cm³

(C) Correct: the data in the Table are not consistent with the hypothesis that as d increases, V_s increases; V_s when d equals 2.7 g/cm³ is greater than V_s when d equals 11.3 g/cm³

(D) Incorrect: although the conclusion that the data are not consistent with the hypothesis is correct, the Table shows that V_s when d equals 11.3 g/cm³ is not greater than V_s when d equals 19.3 g/cm³.