Log out Go to App
Go to App

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

A soprano sings the note \(C 6(1046 \mathrm{~Hz})\) across the mouth of a soda bottle. To excite a fundamental frequency in the soda bottle equal to this note, describe how far the top of the liquid must be below the top of the bottle.

A policeman with a very good ear and a good understanding of the Doppler effect stands on the shoulder of a freeway assisting a crew in a 40 -mph work zone. He notices a car approaching that is honking its horn. As the car gets closer, the policeman hears the sound of the horn as a distinct \(\mathrm{B} 4\) tone \((494 \mathrm{~Hz}) .\) The instant the car passes by, he hears the sound as a distinct \(\mathrm{A} 4\) tone \((440 \mathrm{~Hz}) .\) He immediately jumps on his motorcycle, stops the car, and gives the motorist a speeding ticket. Explain his reasoning.

A bat flying toward a wall at a speed of \(7.0 \mathrm{~m} / \mathrm{s}\) emits an ultrasound wave with a frequency of \(30.0 \mathrm{kHz}\). What frequency does the reflected wave have when it reaches the flying bat?

A classic demonstration of the physics of sound involves an alarm clock in a bell vacuum jar. The demonstration starts with air in the vacuum jar at normal atmospheric pressure and then the jar is evacuated to lower and lower pressures. Describe the expected outcome.

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

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Read Explanation

Rotational Dynamics

Read Explanation

Work Energy and Power

Read Explanation

Oscillations

Read Explanation

Quantum Physics

Read Explanation

Electrostatics

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.

Sign-up for free