Which of the following statements about the speed of sound in different media at around 25 degree Celsius is true? A. In oxygen gas, the speed of sound is 316 km/s. B. In distilled water, the speed of sound is 1498 km/s.

Introduction / Context:
This question checks your conceptual understanding of the speed of sound in different media and the approximate numerical values involved. You are given two statements about the speed of sound in oxygen gas and distilled water at around 25 degree Celsius, but the units are shown in kilometres per second. Your task is to identify which of the statements are true. The key is to recall or estimate the realistic order of magnitude of the speed of sound in gases and liquids.

Given Data / Assumptions:

• Statement A: In oxygen gas, the speed of sound is 316 km/s.
• Statement B: In distilled water, the speed of sound is 1498 km/s.
• Temperature is approximately 25 degree Celsius.
• You may use general physics knowledge about typical speeds of sound in air and water.

Concept / Approach:
The speed of sound in a medium depends on both its elastic properties and its density. In everyday physics, speeds of sound are usually expressed in metres per second, not kilometres per second. The typical speed of sound in air at room temperature is a bit above 300 metres per second, and in water it is about 1500 metres per second. Converting between metres per second and kilometres per second helps quickly show whether the given numerical values are realistic or off by a large factor.

Step-by-Step Solution:
Step 1: Recall the approximate speed of sound in air at room temperature. It is around 340 metres per second, and in pure gases like oxygen it is of the same order, a few hundred metres per second, not hundreds of kilometres per second. Step 2: Convert the given units. Statement A says 316 km/s. Since 1 km/s is 1000 m/s, 316 km/s is 316000 m/s. This is roughly one thousand times larger than the actual typical value for the speed of sound in a gas like oxygen at room temperature. Step 3: Because the realistic value is around a few hundred metres per second, Statement A's claim of 316 kilometres per second is clearly incorrect. It appears that the intended numbers were probably in metres per second, not kilometres per second. Step 4: Now consider Statement B: 1498 km/s in distilled water. Converting units again, 1498 km/s is 1498000 m/s (one million four hundred ninety eight thousand metres per second). The actual speed of sound in water at room temperature is around 1480 to 1500 metres per second, which is three orders of magnitude smaller. Step 5: Just like Statement A, Statement B seems to have used kilometres per second instead of metres per second. The correct order of magnitude is in metres per second, not kilometres per second. Therefore, Statement B is also numerically incorrect as written.

Verification / Alternative check:
Ask yourself whether any everyday physical phenomenon can easily reach speeds on the order of hundreds or thousands of kilometres per second. Such speeds are closer to a significant fraction of the speed of light, which is about 300000 km/s. Sound waves in ordinary media like gases and liquids are much slower, nowhere near these extreme speeds. Because both statements give values that are too large by a factor of roughly 1000, they cannot be true in their given unit form.

Why Other Options Are Wrong:
Option a: “Only statement A is true” is incorrect because Statement A has an unrealistic magnitude for the speed of sound in a gas. Option b: “Both statements A and B are true” is wrong because both statements use kilometres per second where metres per second would be appropriate. Option d: “Only statement B is true” is also incorrect; Statement B suffers from the same unit error. Option e: “The truth of both statements cannot be determined” is not appropriate here, because basic physics knowledge clearly shows that the numerical values are not plausible in the stated units.

Common Pitfalls:
A common mistake is to overlook the units and focus only on the numbers. Since many students memorize approximate speeds like 330 and 1500 without always attaching the metres per second unit, they might incorrectly accept a value expressed in kilometres per second just because the numbers look familiar. Always pay attention to units when evaluating physical quantities; mixing metres per second with kilometres per second leads to errors of a thousand fold.

Final Answer:
Neither statement A nor statement B is true.