Loudness Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Loudness.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

Loudness is how strong or weak a sound seems to a listener.

Bigger wave amplitude usually sounds louder.

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How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Loudness asks what oscillates, what travels, and which wave quantity is being measured.

Common stuck point: Students often know a formula related to loudness but skip the recognition step: Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition?

Worked Examples

Example 1

medium
A sound's intensity rises by a factor of 10001000. How many decibels did the level increase by? (Each 10 dB10\text{ dB} is ×10\times 10.)

Answer

30 dB30\text{ dB}

First step

1
1000=1031000 = 10^3, so three 10 dB10\text{ dB} steps are needed.

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Example 2

medium
Two identical incoherent speakers each produce intensity I0I_0 at a point. What is the combined intensity, and how many decibels louder is this than one speaker alone?

Example 3

medium
Sound A is 40 dB40\text{ dB} and sound B is 40 dB40\text{ dB}, played together (incoherent). What is the combined level?

Example 4

hard
Earplugs reduce sound intensity by a factor of 5050. By how many decibels do they cut the level?

Example 5

hard
A noisy room is at 70 dB70\text{ dB}. An air conditioner adding 66 dB66\text{ dB} on its own is switched on. Estimate the combined dB level. (10−0.4≈0.4010^{-0.4}\approx 0.40.)

Example 6

challenge
A concert at 115 dB115\text{ dB} at 3 m3\text{ m} must drop to 85 dB85\text{ dB} at the back of the venue. How far back is that, assuming a point-source inverse-square law?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Which wave property mainly determines how loud a sound seems?

Example 2

easy
Sound A has larger amplitude than sound B at the same frequency. Which is louder?

Example 3

easy
Does increasing a sound's frequency, with amplitude fixed, make it louder?

Example 4

easy
Loudness is commonly measured in what unit?

Example 5

easy
If a sound wave's amplitude is doubled, does it become louder or quieter?

Example 6

easy
A whisper is about 30 dB and normal speech about 60 dB. Which is louder?

Example 7

easy
Two sounds reach your ear. One has higher amplitude, the other higher frequency. Which one sounds louder (assuming both are audible)?

Example 8

easy
As you walk away from a speaker, the amplitude reaching you drops. What happens to the loudness?

Example 9

medium
Sound intensity is proportional to amplitude squared (I∝A2I\propto A^2). If amplitude triples, by what factor does intensity increase?

Example 10

medium
The sound level rises by 10 dB. Since each 10 dB step multiplies intensity by 10, by what factor does intensity increase?

Example 11

medium
Sound level increases by 20 dB. By what factor does the intensity increase? (Each 10 dB is x10.)

Example 12

medium
A sound at 1 m has intensity 0.8 W/m^2. At 2 m the intensity is one-fourth of that. By the I∝A2I\propto A^2 rule, what fraction of the original amplitude reaches 2 m?

Example 13

medium
Sound intensity at a point is 1.0 W/m^2 from one speaker. A second identical speaker (incoherent) is added at the same distance. What is the total intensity, and how does loudness change qualitatively?

Example 14

medium
A sound's amplitude is halved. Using I∝A2I\propto A^2, what fraction of the original intensity remains?

Example 15

medium
A jackhammer is 100 dB and a library is 40 dB. By what factor is the jackhammer's intensity greater? (Each 10 dB is x10.)

Example 16

medium
At amplitude AA, a wave's intensity is 5 W/m^2. What intensity results if amplitude is increased to 2A2A? (I∝A2I\propto A^2.)

Example 17

medium
A sound's amplitude is tripled. Using I∝A2I\propto A^2, by what factor does its intensity grow?

Example 18

challenge
A sound is 50 dB. To make its intensity 1000 times larger, what dB level is needed? (Each 10 dB is x10.)

Example 19

challenge
A point source gives 70 dB at 1 m. Intensity follows the inverse-square law. What is the dB level at 10 m? (A factor-100 intensity drop is -20 dB.)

Example 20

challenge
Ten identical incoherent machines each produce 60 dB alone at a worker's position. What is the combined sound level? (Intensities add; +10x intensity is +10 dB.)

Example 21

easy
Two tuning forks vibrate at the same frequency. Fork A swings with 0.4 mm0.4\text{ mm} amplitude; fork B swings with 0.1 mm0.1\text{ mm}. Which sounds louder?

Example 22

easy
A speaker plays at 50 dB50\text{ dB}. The volume knob is turned so the level rises to 60 dB60\text{ dB}. By what factor does intensity increase?

Example 23

easy
Rank from quietest to loudest: rustling leaves (20 dB20\text{ dB}), conversation (60 dB60\text{ dB}), rock concert (110 dB110\text{ dB}).

Example 24

easy
A guitar string's vibration amplitude doubles. The intensity of the emitted sound is multiplied by what factor? (I∝A2I\propto A^2)

Example 25

easy
A drum hit gives a sound wave with peak amplitude AA. A softer hit gives A/2A/2. Using I∝A2I\propto A^2, what fraction of the original intensity does the soft hit produce?

Example 26

medium
A fan reads 45 dB45\text{ dB}; a vacuum reads 75 dB75\text{ dB}. By what factor is the vacuum more intense?

Example 27

medium
A sound's amplitude is multiplied by 55. Using I∝A2I\propto A^2, by what factor does intensity grow?

Example 28

medium
A point source produces 80 dB80\text{ dB} at 2 m2\text{ m}. Intensity follows the inverse-square law. What is the level at 20 m20\text{ m}? (A ×100\times 100 intensity drop is −20 dB-20\text{ dB}.)

Example 29

medium
A street has 44 identical incoherent cars each producing 70 dB70\text{ dB} alone at the curb. What is the combined level? (+4×+4\times intensity is +6 dB+6\text{ dB}.)

Example 30

medium
A microphone records a signal whose amplitude is reduced to 30%30\% of its original by a foam pad. What fraction of the original intensity reaches the mic? (I∝A2I\propto A^2)

Example 31

medium
A whisper has intensity 10−10 W/m210^{-10}\text{ W/m}^2 and a normal conversation 10−6 W/m210^{-6}\text{ W/m}^2. The conversation is louder by how many decibels?

Example 32

medium
A pressure wave's amplitude is 0.2 Pa0.2\text{ Pa}. A second wave with the same frequency has amplitude 0.6 Pa0.6\text{ Pa}. How many times more intense is the second?

Example 33

hard
A factory hits 90 dB90\text{ dB} at 5 m5\text{ m} from a machine. Using the inverse-square law for a point source, find the level at 50 m50\text{ m}.

Example 34

hard
A sound at 60 dB60\text{ dB} must be made 1000010000 times more intense for an experiment. What is the new dB level?

Example 35

hard
A speaker at 1 m1\text{ m} measures 85 dB85\text{ dB}. You move to 4 m4\text{ m}. What is the new level? (Point-source inverse square; log⁡10(16)≈1.20\log_{10}(16)\approx 1.20.)

Example 36

hard
Two incoherent fans each give 50 dB50\text{ dB}; a third identical fan turns on. What is the new combined level? (+50%+50\% intensity from 2 to 3 fans.)

Example 37

hard
A sound has intensity I0=10−12 W/m2I_0=10^{-12}\text{ W/m}^2 (threshold of hearing) and another has 1 W/m21\text{ W/m}^2 (threshold of pain). Find the dB level of the pain threshold using L=10log⁡10(I/I0)L=10\log_{10}(I/I_0).

Example 38

challenge
A point-source siren reads 100 dB100\text{ dB} at 10 m10\text{ m}. Safety guidelines cap continuous exposure at 80 dB80\text{ dB}. How far away must you stand (inverse-square law)?

Example 39

challenge
Twenty identical incoherent machines each produce 75 dB75\text{ dB} alone at a worker's ear. What is the combined level? (log⁡10(20)≈1.30\log_{10}(20)\approx 1.30.)
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Related Concepts

SoundIntensity

Background Knowledge

These ideas may be useful before you work through the harder examples.

soundintensity