/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 2 A sound level of 50 decibels is ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

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: The intensity of a 50-decibel sound is 1000 times as intense as a sound of 20 decibels.

Step by step solution

01

Write the given values and formula

We know that: - A 50-decibel sound has a decibel level of 50 dB - A 20-decibel sound has a decibel level of 20 dB The formula to convert decibel levels to intensities is: \( dB = 10 \times log_{10}(\frac{I}{I_0}) \)
02

Find the ratio of intensities#

First, let's consider the 50-decibel sound. Let \(I_1\) be its intensity. Using the formula, we have: \( 50 = 10 \times log_{10}(\frac{I_1}{I_0}) \) Now consider the 20-decibel sound. Let \(I_2\) be its intensity. Using the formula, we have: \( 20 = 10 \times log_{10}(\frac{I_2}{I_0}) \) We need to find the ratio \(\frac{I_1}{I_2}\).
03

Solve the equations for \(I_1\) and \(I_2\)

First, divide both sides of the equations by 10: \( 5 = log_{10}(\frac{I_1}{I_0}) \) \( 2 = log_{10}(\frac{I_2}{I_0}) \) Now, eliminate the logarithms using the property \(a = log_{10}(b) \Rightarrow b = 10^a\): \( I_1 = I_0 \times 10^5 \) \( I_2 = I_0 \times 10^2 \)
04

Calculate the intensity ratio

The intensity ratio between the two sounds can be found by dividing \(I_1\) by \(I_2\): \( \frac{I_1}{I_2} = \frac{I_0 \times 10^5}{I_0 \times 10^2} \) Simplify the expression by canceling the \(I_0\) terms: \( \frac{I_1}{I_2} = \frac{10^5}{10^2} \) Now, use the property \( \frac{a^b}{a^c} = a^{b-c}\) for exponents: \( \frac{I_1}{I_2} = 10^{(5-2)} \) \( \frac{I_1}{I_2} = 10^3 \) Thus, the intensity of a 50-decibel sound is 1000 times as intense as a sound of 20 decibels.
05

Select the correct answer

The intensity ratio \(\frac{I_1}{I_2}\) is 1000, which corresponds to option (e). Hence, the correct answer is: e) 1000 times as intense as a sound of 20 decibels.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Electromagnetic radiation (light) consists of waves. More than a century ago, scientists thought that light, like other waves, required a medium (called the ether) to support its transmission. Glass, having a typical mass density of \(\rho=2500 \mathrm{~kg} / \mathrm{m}^{3},\) also supports the transmission of light. What would the elastic modulus of glass have to be to support the transmission of light waves at a speed of \(v=2.0 \cdot 10^{8} \mathrm{~m} / \mathrm{s} ?\) Compare this to the actual elastic modulus of window glass, which is \(5 \cdot 10^{10} \mathrm{~N} / \mathrm{m}^{2}\).

The Moon has no atmosphere. Is it possible to generate sound waves on the Moon?

You are traveling in a car toward a hill at a speed of \(40.0 \mathrm{mph} .\) The car's horn emits sound waves of frequency \(250 \mathrm{~Hz},\) which move with a speed of \(340 \mathrm{~m} / \mathrm{s}\) a) Determine the frequency with which the waves strike the hill. b) What is the frequency of the reflected sound waves you hear? c) What is the beat frequency produced by the direct and the reflected sounds at your ears?

Two people are talking at a distance of \(3.0 \mathrm{~m}\) from where you are, and you measure the sound intensity as \(1.1 \cdot 10^{-7} \mathrm{~W} / \mathrm{m}^{2}\). Another student is \(4.0 \mathrm{~m}\) away from the talkers. What sound intensity does the other student measure?

A half-open pipe is constructed to produce a fundamental frequency of \(262 \mathrm{~Hz}\) when the air temperature is \(22^{\circ} \mathrm{C} .\) It is used in an overheated building when the temperature is \(35^{\circ} \mathrm{C} .\) Neglecting thermal expansion in the pipe, what frequency will be heard?
See all solutions

Recommended explanations on Physics Textbooks

Engineering Physics

Read Explanation

Turning Points in Physics

Read Explanation

Scientific Method Physics

Read Explanation

Famous Physicists

Read Explanation

Electric Charge Field and Potential

Read Explanation

Waves Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.