/*! 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 12 A sound wave from a siren has an... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Problem 12

A sound wave from a siren has an intensity of \(100.0 \mathrm{~W} / \mathrm{m}^{2}\) at a certain point, and a second sound wave from a nearby ambulance has an intensity level \(10 \mathrm{~dB}\) greater than the siren's sound wave at the same point. What is the intensity level of the sound wave due to the ambulance?

Short Answer

Expert verified
The intensity level of the sound wave due to the ambulance is 1000 W/m虏.

Step by step solution

01

Write down the given values and formula to use

We know the intensity \(I_1 = 100 W/m^2\) of the initial sound and the change in dB \(\Delta dB = 10 dB\). The formula to use is: \(\Delta dB = 10 \log_{10} \left( \frac{I_2}{I_1}\right)\)
02

Rearrange formula to isolate \(I_2\)

Rearrange the formula to get \(I_2\) on one side: \(I_2 = I_1 \cdot 10^{(\Delta dB / 10)}\)
03

Substitute known values into the equation and solve

Substitute \(I_1 = 100 W/m^2\) and \(\Delta dB = 10 dB\) into the equation from step 2 and solve for \(I_2\). Therefore, \(I_2 = 100 W/m^2 \cdot 10^{(10 / 10)} = 1000 W/m^2\)

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Decibel Scale
The decibel (dB) scale is a logarithmic way of expressing sound intensity. It measures the loudness level by comparing it to a reference level, simplifying complex calculations. This scale is particularly useful in acoustic physics since sound intensity changes exponentially.

The decibel scale operates on a base-10 logarithm. So, each 10 dB increase represents a tenfold increase in intensity. For instance, a sound that is 10 dB louder is ten times more intense in its power. Hence, an increase from 100 dB to 110 dB means the sound intensity is multiplied by ten.

The use of the decibel scale helps in managing the wide range of sound levels encountered in nature and technology. It provides an intuitive way of understanding how sound intensity levels can impact us.
Performing Logarithmic Calculations
Logarithmic calculations are essential in interpreting and working with the decibel scale. The formula that relates sound intensity and its decibel measure is given by:
  • \( \,\text{dB} = 10 \log_{10}(\frac{I}{I_0}) \)
where \(I_0\) is a reference intensity, typically the threshold of hearing \( 10^{-12} \mathrm{~W/m^2} \) in air.

When you're dealing with logarithmic functions, understand that they are the inverse of exponential functions. This means that increasing the intensity by a factor results in a simple addition in the decibel scale.

To solve for a change in intensity, rearrange the formula to solve for the final intensity, \( I \), using:
  • \( I_f = I_i \cdot 10^{(\Delta \text{dB}/10)} \)
Logarithmic calculations can seem challenging, but they effectively simplify vastly different scales of measurement.
Exploring Acoustic Physics
Acoustic physics encompasses the study of sound waves, their production, transmission, and effects. Sound is a mechanical wave that requires a medium (like air, water, or solids) to travel.

Intensity in acoustics refers to the power per unit area carried by the wave, measured in watts per square meter \( \mathrm{W/m^2} \). Sound intensity depends on the wave's amplitude and frequency, where higher intensity sounds are often perceived as louder.

Sound waves can vary greatly in intensity. This variability is why sound needs to be measured using a scale like decibels that can handle the many orders of magnitude sound waves can have in intensity.

Detection and measurement of sound intensity are crucial in various fields. It is vital in environments like urban planning, designing concert halls, or setting up audio devices, where controlling sound levels can affect people's experience and health.

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

\(A\) quartz watch contains a crystal oscillator in the form of a block of quartz that vibrates by contracting and expanding. Two opposite faces of the block, \(7.05 \mathrm{~mm}\) apart, are antinodes, moving alternately toward and away from each other. The plane halfway between these two faces is a node of the vibration. The speed of sound in quartz. is \(3.70 \mathrm{~km} / \mathrm{s}\). Find the frequency of the vibration. An oscillating electric voltage accompanies the mechanical

A pair of speakers connected to the same sound system face each other, one at \(x=0\) and the other at \(x=4.00 \mathrm{~m}\). If they are playing a sound with frequency \(343 \mathrm{~Hz}\), what are the points of constructive interference between the two speakers? (Take the speed of sound as \(343 \mathrm{~m} / \mathrm{s}\).)

The human ear canal is about \(2.8 \mathrm{~cm}\) long. If it is regarded as a tube that is open at one end and closed at the eardrum, what is the fundamental frequency around which we would expect hearing to be most sensitive? Take the speed of sound to he \(340 \mathrm{~m} / \mathrm{s}\).

ecp A standing wave is set up in a string of variable length and tension by a vibrator of variable frequency. Both ends of the string are fixed. When the vibrator has a frequency \(f_{A}\), in a string of length \(L_{4}\) and under tension \(T_{1}, n_{A}\) antinodes are set up in the string. (a) Write an expression for the frequency \(f_{A}\) of a standing wave in terms of the number \(n_{A}\), length \(L_{\cdot+}\), tension \(T_{A}\), and linear density \(\mu_{A}\). (b) If the length of the string is doubled to \(L_{h}=2 L_{A}\), what frequency \(f_{B}\) (written as a multiple of \(f_{A}\) ) will result in the same number of antinodes? Assume the tension and linear density are unchanged. Hint Make a ratio of expressions for \(f_{b}\) and \(f_{A^{\prime}}(\mathrm{c})\) If the frequency and length are held constant, what tension \(T_{g}\) will produce \(n_{A}+1\) antinodes? (d) If the frequency is tripled and the length of the string is halved. by what factor should the tension be changed so that twice as many antinodes are produced:

A tumnel under a river is \(2.00 \mathrm{~km}\) long. (a) At what frequencies can the air in the tunnel resonate? (b) Explain whether it would be good to make a rule against blowing your car horn when you are in the tunnel.
See all solutions

Recommended explanations on Physics Textbooks

Measurements

Read Explanation

Famous Physicists

Read Explanation

Physical Quantities And Units

Read Explanation

Electric Charge Field and Potential

Read Explanation

Oscillations

Read Explanation

Energy 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.