To accurately determine whether the statements regarding the average speed of sound in gas, liquid, and solid are true, we first need to consider typical values for the speed of sound in these states of matter:
- Average speed of sound in air (gas): approximately 343 m/s at room temperature.
- Average speed of sound in water (liquid): approximately 1482 m/s.
- Average speed of sound in steel (solid): approximately 5960 m/s.
Now, let's calculate the ratios needed for each of the statements.
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The average speed of sound in a liquid is about 3.7 times the average speed of sound in a gas. \[ \frac{v_{liquid}}{v_{gas}} = \frac{1482 , \text{m/s}}{343 , \text{m/s}} \approx 4.32 \] This statement is FALSE.
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The average speed of sound in a solid is about 13.9 times the average speed of sound in a gas. \[ \frac{v_{solid}}{v_{gas}} = \frac{5960 , \text{m/s}}{343 , \text{m/s}} \approx 17.38 \] This statement is FALSE.
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The average speed of sound in a solid is about 0.07 times the average speed of sound in a gas. \[ \frac{v_{solid}}{v_{gas}} = \frac{5960 , \text{m/s}}{343 , \text{m/s}} \approx 17.38 \] This statement is FALSE.
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The average speed of sound in a solid is about 3.7 times the average speed of sound in a liquid. \[ \frac{v_{solid}}{v_{liquid}} = \frac{5960 , \text{m/s}}{1482 , \text{m/s}} \approx 4.02 \] This statement is FALSE.
Based on these calculations, none of the provided statements regarding the average speed of sound in gas, liquid, and solid are true.