To the nearest order of magnitude, how many times greater than the speed of sound is the speed of light?
104
106
1010
1012
106
To find the nearest order of magnitude of the speed of light compared to the speed of sound, we need to calculate the ratio of their speeds.
The speed of sound is approximately 343 meters per second, while the speed of light in a vacuum is approximately 299,792,458 meters per second.
To calculate the ratio, we divide the speed of light by the speed of sound:
Ratio = (speed of light) / (speed of sound)
Ratio ≈ 299,792,458 m/s / 343 m/s
Simplifying this gives us:
Ratio ≈ 874,030
Now, we need to determine the order of magnitude of this ratio. Order of magnitude is the power of 10 nearest to a given quantity.
To do this, we express the ratio in scientific notation. In scientific notation, a number is written as a decimal between 1 and 10, multiplied by a power of 10.
Ratio ≈ 8.74030 x 10^5
From this, we can observe that the order of magnitude is 10^5, since the number is multiplied by 10 to the power of 5.
To find which option among 104, 106, 1010, and 1012 is closest to the order of magnitude, we compare the exponents of 10:
- The exponent 10^4 is one less than 10^5, so it is not the nearest order of magnitude.
- The exponent 10^6 is one greater than 10^5, so it is greater than the order of magnitude.
- The exponent 10^10 is five greater than 10^5, so it is much greater than the order of magnitude.
- The exponent 10^12 is seven greater than 10^5, so it is also much greater than the order of magnitude.
Hence, the option closest to the order of magnitude is 10^5, which corresponds to the answer being 106.