You are on an island where a huge explosion at a distance of 915 miles away can be heard. How long (in seconds) does it take the sound to travel to your location? Assume the temperature of the air is 20 oC
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To determine how long it takes for sound to travel from a distance of 915 miles to your location, we need to consider the speed of sound and the temperature of the air. The speed of sound depends on the temperature of the air.
At 20 oC, the speed of sound is approximately 343 meters per second (m/s) or 1125 feet per second (ft/s).
First, we need to convert the distance from miles to meters or feet:
915 miles = 1470592 meters (1 mile = 1609.34 meters)
915 miles = 4792800 feet (1 mile = 5280 feet)
Now, we can calculate the time it takes for sound to travel from that distance:
Time = Distance / Speed
Using meters:
Time = 1470592 meters / 343 m/s
Time ≈ 4289.6 seconds
Using feet:
Time = 4792800 feet / 1125 ft/s
Time ≈ 4266.9 seconds
Therefore, it takes approximately 4289.6 seconds (or about 71 minutes and 30.6 seconds) for the sound to travel from a distance of 915 miles to your location at 20 oC.
To calculate the time it takes for sound to travel to your location, we need to know the speed of sound in air, which depends on the temperature. The speed of sound in dry air at a temperature of 20 oC is approximately 343 meters per second (m/s).
First, we need to convert the distance from miles to meters, as the speed of sound is given in meters per second. To convert miles to meters, we use the conversion factor 1 mile = 1609.34 meters.
Distance in meters = 915 miles × 1609.34 meters/mile ≈ 1,472,472 meters.
Next, we divide the distance by the speed of sound to find the time it takes for the sound to travel:
Time = Distance / Speed
Time = 1,472,472 meters / 343 m/s ≈ 4291.15 seconds.
Therefore, it takes approximately 4291.15 seconds (or about 71.52 minutes) for the sound to travel from the explosion to your location on the island at a temperature of 20 oC.