Question

Volume and decibels When the volume control on a stereo system is increased, the voltage across a loudspeaker changes from $V_{1}$ to $V_{2},$ and the decibel increase in gain is given by $$ \mathrm{db}=20 \log \frac{V_{2}}{V_{1}} $$ Find the decibel increase if the voltage changes from 2 volts to 4.5 volts.

Name: Problem 51, Chapter 4: Precalculus: Functions and Graphs
Uploaded: 2021-05-25T14:54:56-08:00
Duration: 1 min 4 s
Channel: Christopher Stanley
Description: Volume and decibels When the volume control on a stereo system is increased, the voltage across a loudspeaker changes from V1 to V2, and the decibel increase in gain is given by db=20 log(V2)/(V1) Find the decibel increase if the voltage changes from 2 volts to 4.5 volts.

   Volume and decibels When the volume control on a stereo system is increased, the voltage across a loudspeaker changes from $V_{1}$ to $V_{2},$ and the decibel increase in gain is given by
$$
\mathrm{db}=20 \log \frac{V_{2}}{V_{1}}
$$
Find the decibel increase if the voltage changes from 2 volts to 4.5 volts.

Precalculus: Functions and Graphs

Earl W. Swokowski,… 11th Edition

Chapter 4, Problem 51

Instant Answer

Solved by Expert Christopher Stanley

05/25/2021

Step 1

Step 1: We are given the formula for decibel increase as $$ \mathrm{db}=20 \log \frac{V_{2}}{V_{1}} $$ where $V_{1}$ and $V_{2}$ are the initial and final voltages across the loudspeaker respectively. Show more…

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Volume and decibels When the volume control on a stereo system is increased, the voltage across a loudspeaker changes from $V_{1}$ to $V_{2},$ and the decibel increase in gain is given by $$ \mathrm{db}=20 \log \frac{V_{2}}{V_{1}} $$ Find the decibel increase if the voltage changes from 2 volts to 4.5 volts.

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Key Concepts

Decibels

Decibels are a logarithmic unit used to describe ratios, such as the gain in voltage or power in electronic systems. This unit is particularly handy for comparing quantities that vary over a wide range of values, as it compresses large ratios into a more manageable and interpretable scale.

Voltage Ratio and Gain

The voltage ratio is a measure of change in voltage between two states of a system, commonly used to indicate gain in amplifiers or audio systems. The ratio of output to input voltage is key to computing the gain and subsequently expressing that gain in decibels.

Logarithmic Scale and Logarithms

The use of a logarithmic scale in decibel calculations is essential because it translates multiplicative changes in voltage into additive values. By taking 20 times the logarithm (base 10) of the voltage ratio, small changes in voltage can be more easily analyzed and compared, reflecting how humans perceive changes in loudness.

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