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Chapter 16: Problem 2

A sound level of 50 decibels is a) 2.5 times as intense as a sound of 20 decibels. b) 6.25 times as intense as a sound of 20 decibels. c) 10 times as intense as a sound of 20 decibels. d) 100 times as intense as a sound of 20 decibels. e) 1000 times as intense as a sound of 20 decibels.

Short Answer

Expert verified
Answer: (e) The 50-decibel sound is 1000 times as intense as the 20-decibel sound.

Step by step solution

01

Understand the decibel formula

The decibel (dB) scale is used to quantify the intensity of sound and is defined as 10 times the logarithm of the ratio of the intensity (I) of the sound to the reference intensity (I0). The formula for decibels is: dB = 10 * log(I / I0).
02

Calculate the intensity for both 20 decibels and 50 decibels

In order to compare the intensities of 20 decibels and 50 decibels, first, we need to find the ratio of the intensities for both using the decibel formula: For 20 decibels: 20 = 10 * log(I1 / I0) => I1 / I0 = 10^(20/10) => I1 / I0 = 10^2 For 50 decibels: 50 = 10 * log(I2 / I0) => I2 / I0 = 10^(50/10) => I2 / I0 = 10^5
03

Calculate the ratio of intensities for the 50-decibel sound and the 20-decibel sound

Now, we have the intensity ratios for both sounds with respect to the reference intensity (I0). Next, we need to find how many times the intensity of the 50-decibel sound is greater than the 20-decibel sound. To do this, we divide the intensity ratio of the 50-decibel sound by the intensity ratio of the 20-decibel sound: Intensity ratio = (I2 / I0) / (I1 / I0) = I2 / I1 = (10^5) / (10^2) = 10^3
04

Conclusion

The ratio of intensities between the 50-decibel sound and the 20-decibel sound is 10^3. So, the 50-decibel sound is 1000 times as intense as the 20-decibel sound. The correct answer is choice (e).

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Most popular questions from this chapter

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