Final answer:
To calculate the time interval of an echo on a 15°C day, the speed of sound at this temperature (340 m/s) is used to divide the round-trip distance. Without the total distance for the sound to travel, it's not possible to determine the specific time interval from the provided choices.
Step-by-step explanation:
To determine the time interval for the echo of a clap that a girl measures on a cold day of temperature 15°C, we need to know the speed of sound in air at that temperature. The speed of sound in air varies with temperature, and a rough estimate is that sound travels at 343 m/s at 20°C. Temperature can affect this speed roughly at a rate of 0.6 m/s per degree Celsius change. Since the temperature in question is 15°C, which is 5°C below 20°C, we reduce the speed of sound accordingly.
The adjusted speed of sound, vsound, is:
vsound = 343 m/s - (5°C × 0.6 m/s/°C) = 343 m/s - 3 m/s = 340 m/s.
If we assume the girl heard the echo after a round trip of the sound wave (the sound travels to the reflective surface and then back to her), and if the total distance covered by the sound wave is known (which, according to the example provided, would likely be 6.00 m), then the time interval, t, taken for the echo can be calculated using the formula:
t = distance / speed = 6.00 m / 340 m/s = 0.0176 s (round trip).
Since this question does not provide the total distance the sound traveled, it's not possible to determine the specific answer to the given choices (a through d) without that information.