Monday, June 27, 2011

Practice with logarithmic scales - Richter and decibel.

a) There was a 7.6 earthquake in Mindanao in the Philippines and a 5.7 aftershock three days later. Rounded to the nearest multiple of 10, how much stronger was the bigger quake?

b) An earthquake registering 5.7 is recorded one morning, and in the afternoon, another quake 27 times stronger is felt. Give the Richter reading of the second stronger quake. (Nearest tenth.)

c) What is the decibel reading of a sound that has 7 times more energy than a 75 decibel reading. (Nearest decibel.)

d) One singer is measured at 64 dB. Eight singers at the same level would have eight times more energy. To the nearest decibel, what is the decibel level of the eight singer chorus?

e)  How much more energy is there in a reading of 75 dB compared to 64 dB.  Round to the nearest whole number.

Answers in the comments.

1 comment:

Prof. Hubbard said...

a) There was a 7.6 earthquake in Mindanao in the Philippines and a 5.7 aftershock three days later. Rounded to the nearest multiple of 10, how much stronger was the bigger quake?

Step 1: 7.6 - 5.7 = 1.9

Step 2: 1.9 * 1.5 = 2.85

Step 3: 10^2.85 = 707.94578...

If we rounded to the nearest whole number, the answer would be 708. But because the Richter rounding to the nearest multiple of ten, we should round to just one significant digit and say the larger quake is about 700 times stronger.



b) An earthquake registering 5.7 is recorded one morning, and in the afternoon, another quake 27 times stronger is felt. Give the Richter reading of the second stronger quake. (Nearest tenth.)

Step 1: log(27) = 1.4313...,

Step 2: divide by 1.5 to get .954..., which we round to 1.0.

Step 2: 5.7 + 1.0 = 6.4, so the stronger quake has a Richter scale reading of 6.4

c) What is the decibel reading of a sound that has 7 times more energy than a 75 decibel reading. (Nearest decibel.)

Step 1: log(7) = 0.845..., which rounds to 0.8 bels, which is the same as 8 decibels.

Step 2: 75 + 8 = 83, so the louder sound has a reading of 83 dB.

d) One singer is measured at 64 dB. Eight singers at the same level would have eight times more energy. To the nearest decibel, what is the decibel level of the eight singer chorus?

Step 1: log(8) = 0.903089..., which rounds to 0.9 bel or 9 decibels.

Step 2: 64 + 9 = 73, so the louder sound has a reading of 73 dB.



e) How much more energy is there in a reading of 75 dB compared to 64 dB. Round to the nearest whole number.

Step 1: 75 - 64 = 11, so the difference is decibels is 11.

Step 2: 11 db = 1.1 bels

Step 3: 10^1.1 = 12.589..., so rounding to the nearest whole number, we would say the 75 dB sound is 13 times stronger than the 64 dB sound.