Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration


College Physics (Urone)
Found in: Page 595

Answers without the blur.

Just sign up for free and you're in.


Short Answer

Loudspeakers can produce intense sounds with surprisingly small energy input in spite of their low efficiencies. Calculate the power input needed to produce a \(90.0\;{\rm{dB}}\) sound intensity level for a \({\rm{12}}{\rm{.0}}\;{\rm{cm}}\)diameter speaker that has an efficiency of \(1.00\% \). (This value is the sound intensity level right at the speaker.)

The input power is\(1.767 \times {10^{ - 3}}\;{\rm{W}}\).

See the step by step solution

Step by Step Solution

Intensity of Sound

The intensity of sound depends on the amplitude, and the loudness is the effect of intensity on human ears.

Given Data

The sound intensity is\(90.0\;{\rm{dB}}\).

The diameter of the speaker is\(12.0\;{\rm{cm}}\).

The efficiency is\(1.00\% \).

Calculation of the power of the sound

The intensity of the unaided hearing is,

\({{\rm{d}}_{\rm{1}}}{\rm{ = 10log}}\frac{{{{\rm{I}}_{\rm{0}}}}}{{{\rm{1}}{{\rm{0}}^{{\rm{12}}}}}}\)and\({I_0} = {10^{12}}\;{\rm{W/}}{{\rm{m}}^{\rm{2}}}\).


\(\begin{array}{c}90 = 10\log \frac{{{I_0}}}{{{{10}^{ - 12}}}}\\9 = \log \frac{{{I_0}}}{{{{10}^{ - 12}}}}\\{I_0} = {10^9} \times {10^{ - 12}}\\{I_0} = {10^{ - 3}}\end{array}\)

The power output is,

\(\begin{array}{c}P = {I_0}A\\P = {10^{ - 3}} \times \pi \times {\left[ {\frac{{0.15}}{2}} \right]^2}\\P = 1.767 \times {10^{ - 5}}\;{\rm{W}}\end{array}\)

The input power is,

\(\begin{array}{c}P' = \frac{P}{{efficiency}}\\ = \frac{{1.767 \times {{10}^{ - 5}}}}{{0.01}}\\ = 1.767 \times {10^{ - 3}}\;{\rm{W}}\end{array}\)

The input power is\(1.767 \times {10^{ - 3}}\;{\rm{W}}\).


Want to see more solutions like these?

Sign up for free to discover our expert answers
Get Started - It’s free

Recommended explanations on Physics Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.