# Sound power: What is 100mW amplified by 2dB?

• dbag123
In summary, 100mW equals 20 dBm and is then amplified by 2dB. This results in a power output of 110mW, not 10mW as previously thought. The unit dB is a logarithmic scale used for measuring amplification, and a 2dB amplification will increase power by a factor of 1.585. This concept was first introduced by Alexander Graham Bell in his study of sound intensity.
dbag123
Homework Statement
Signal rated at 100mW is amplified by 2dB. How much is the power out of the amplifier
Relevant Equations
i=10lg(I/I0)db
100mW = 20 dBm, that is then amplified by 2dB

20dBm/2dB = 10mW so power out of the amplifier would be 100mW+10mW =110mW?

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dbag123 said:
Homework Statement: Signal rated at 100mW is amplified by 2dB. How much is the power out of the amplifier
Homework Equations: i=10lg(I/I0)db

100mW = 20 dBm, that is then amplified by 2dB

20dBm/2dB = 10mW so power out of the amplifier would be 100mW+10mW =110mW?
dB in general and dBm in particular are logarithmic scales. Dividing dBm by dB does not make the kind of sense you expect.

20dBm/2dB gives a result of "10". But not 10 mW. The "10" that it yields is the number of times you would need to apply a 2dB amplification to amplify a 0 dBm (1 mW) signal to 20dBm (100 mW).

Each such amplification step would multiply power by the same factor as every other step.

allright. how do i get this problem started?

dbag123 said:
allright. how do i get this problem started?
Do you know what it means to amplify something by 2dB?

Or, simpler -- do you know what it means to amplify something by 1B?

increase the intensity levels of sound

dbag123 said:
increase the intensity levels of sound
Not really. If you are learning from a textbook, you should take time to go back and look at the definition. Or use Google.

The unit is not specific to sound. It can be used for anything.

1 Bell is an amplification by a factor of 10.
2 Bells is an amplification by a factor of 100.
3 Bells is an amplification by a factor of 1000.

In general, if 0 B is the base level on [whatever quantity you are measuring], x B is ##10^x## times that much.

One dB is one tenth of a B. If 0 dB is the base level on [whatever quantity you are measuring], x dB is ##10^{x/10}## times that much.

so a 2 dB amplification would multiply the power by 1,585

jbriggs444
dbag123 said:
so a 2 dB amplification would increase the power by 1,585
Bingo.

dbag123 said:
interesting. i am not learning from a book, just some course notes, the term Bell is not mentioned anywhere in these notes.
The story I learned from my father many years ago and which I may have embellished a bit myself [so take it with a grain of salt] is that Alexander Graham Bell was studying sound and came up with a scale for intensity.

0 for inaudible silence.
1 for the softest barely audible sound
2 for something detectably louder than that
3 for something detectably louder than that
and so on.

He discovered that human hearing was approximately logarithmic. By the time you had 10 detectable increments in loudness, you'd increased signal power by a factor of ten. So each detectable increment in loudness was approximately a factor of ##^{10}\sqrt{10}## increase in power.

The name taken for the factor of 10 was Bell and the name for the smallest audible increment in loudness then becomes one tenth of a Bell -- the decibel.

By happy coincidence, 3 dB is very nearly a factor of 2. Handy engineering approximation.

thank you very much. any chance i could borrow you for another problem? it has to do with sound dampening through an object. the question is does that object dampen the sound by 1 or by 2 due to the mediums it has to pass

dbag123 said:
thank you very much. any chance i could borrow you for another problem? it has to do with sound dampening through an object. the question is does that object dampen the sound by 1 or by 2 due to the mediums it has to pass
Go ahead and start a new thread with your new question. Be sure to make a complete, clear problem statement (including a diagram if you have one), and show your attempt at the solution. That's the best way to get help on schoolwork questions here.

## 1. What is sound power?

Sound power is the amount of energy per unit of time that is radiated by a sound source in all directions.

## 2. What is 100mW?

100mW (milliwatt) is a unit of power that is equal to one-thousandth of a watt. It is commonly used to measure the power output of electronic devices such as speakers and headphones.

## 3. What does it mean to amplify sound by 2dB?

Amplifying sound by 2dB means increasing the sound power or volume level by 2 decibels. This results in a slight increase in loudness, but may not be noticeable to the human ear.

## 4. How does amplification affect sound power?

Amplification increases the sound power by a certain amount, depending on the amount of amplification. For example, a 2dB amplification will result in a doubling of the sound power, while a 10dB amplification will result in a 10-fold increase in sound power.

## 5. Is a 2dB amplification significant?

It depends on the context. In a quiet room, a 2dB amplification may be noticeable, but in a loud concert, it may not make much of a difference. However, in terms of sound power, a 2dB amplification is a significant increase.

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