A question answer community on a mission

to share Solutions for all STEM major Problems.

to share Solutions for all STEM major Problems.

Cant find a problem on ToughSTEM?

0

The volume control on a surround-sound amplifier is adjusted so the sound intensity level at the listening position increases from 23 to 61 dB. What is the ratio of the final sound intensity to the original sound intensity?

Added Tue, 04 Aug '15

Community

1

Add a Comment

Solutions

0

The decibel scale is defined as

beta = 10*log_10(I/I0)

Apply subscripts 1 and 2 to correspond to the conditions given:

beta1 = 10*log_10(I1/I0)

beta2 = 10*log_10(I2/I0)

Subtract (you will see why), beta2 - beta1:

beta2 - beta1 = 10*(log_10(I2/I0) - log_10(I1/I0))

Combining the logarithm, and you get:

beta2 - beta1 = 10*log_10(I2/I1)

Solve for the ratio of I's:

(beta2 - beta1)/10 = log_10(I2/I1)

Exponentiate both sides with base 10:

10^((beta2 - beta1)/10) = I2/I1

Thus:

I2/I1 = 10^((beta2 - beta1)/10)

Data:

beta2:=61 dB; beta1:=23 dB;

Result:

I2/I1 = 6309.57

Added Tue, 04 Aug '15

Community

1

Add a Comment

Add Your Solution!

Close

Click here to

Choose An Image

or

Get image from URL

GO

Close

Back

Add Image

Close

What URL would you like to link?

GO

α

β

γ

δ

ϵ

ε

η

ϑ

λ

μ

π

ρ

σ

τ

φ

ψ

ω

Γ

Δ

Θ

Λ

Π

Σ

Φ

Ω

∫

∮

∞

∝

∇

∴

→

↔

⊆

⊂

∀

∃

∈

∉

∪

∩

∅

Copied to Clipboard

Sign Up

to interact with the community. (That's part of how we ensure only good content gets on ToughSTEM)

OR

OR

ToughSTEM is completely free, and its staying that way. Students pay way too much already.

Almost done!

Please **check your email** to finish creating your account!

Welcome to the Club!

Choose a new Display Name

Only letters, numbers, spaces, dashes, and underscores, are allowed. Can not be blank.

Great! You're all set, .

A question answer community on a mission

to share Solutions for all STEM major Problems.

to share Solutions for all STEM major Problems.

Why

The Purpose

The Purpose

How

The Community

The Community

Give Feedback

Tell us suggestions, ideas, and any bugs you find. Help make ToughSTEM even better.