# 1kHz comfortable listening amplitude

Discussion in 'Homework Help' started by J_Rod, Feb 13, 2015.

1. ### J_Rod Thread Starter Member

Nov 4, 2014
109
6
Hi all,
Came across this question and I was wondering if you know what the peak to peak amplitude for comfortable listening is of an AC signal with frequency 1kHz.
Thanks for sharing

2. ### #12 Expert

Nov 30, 2010
17,897
9,316
This is impossible to answer because we don't know the efficiency of the speaker.
However, you might try for 70db to 80db as, "comfortable".

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3. ### J_Rod Thread Starter Member

Nov 4, 2014
109
6
Ah, okay, thanks. I was supposed to measure the amplitude on an oscilloscope in terms of a peak to peak voltage. How can I convert avg. 75 dB to units voltage gain? I looked up dB = 20 log(V2/V1), so would it be:

75 db = 20 log(gain)
10^(75/20) = gain =~ 5.6kV

4. ### #12 Expert

Nov 30, 2010
17,897
9,316
You are completely out of the ball park. The missing part is how much sound the speaker makes for a certain voltage of input. Without that, you have nothing. I have seen speakers rated for 78 db for one watt at one meter of distance and 103 db at one watt of input and one meter of distance. Suppose you have a really awful Radio Shack speaker at 78 db per watt. What voltage puts one watt into an 8 ohm speaker?

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5. ### J_Rod Thread Starter Member

Nov 4, 2014
109
6
P = V^2 /R
V = (RP)^0.5
V = (8ohm *1W)^0.5 =~ 2.82V
So 2.8V is the potential difference needed for the speaker to produce 78dB per W consumed at one meter distance. Then if 75 dB is a comfortable listening level,
2.82V/78dB = v/75dB
v = 2.82 *75/78 V =~ 2.7V
But would peak to peak for AC mean 5.4V is the needed voltage? By the way the speaker looked like a really cheap one...

6. ### #12 Expert

Nov 30, 2010
17,897
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2.82 volts is the RMS value. You have to convert that to peak-to-peak.
You forgot the square root of 2 to get from RMS to peak.
NOW you use db = 20 log (V2/V1)

7. ### J_Rod Thread Starter Member

Nov 4, 2014
109
6
VRMS = Vpeak/2^0.5 = 2^1.5
Vpeak = 2^2 = 4V
Hmm.. so peak to peak voltage is 8V ? Then the dB level is 20 log 8 =~ 18dB... doesn't make sense...

8. ### #12 Expert

Nov 30, 2010
17,897
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p-p = rms x 2 x radical 2
75db is 3 db less than 78 db
-3db = 20 log V2/V1

9. ### J_Rod Thread Starter Member

Nov 4, 2014
109
6
The output voltage is 8V needed to drive the speaker, right? So solving for input voltage using the voltage gain equation will give the peak to peak amplitude of the input wave at 1kHz.
75dB -78dB = 20 log(8/V)
-3/20 = log(8/V)
10^(-3/20) = 8/V
V = 8 *10^(3/20) =~ 11.3V

10. ### #12 Expert

Nov 30, 2010
17,897
9,316
PR = E^2
1W x 8 ohms = E^2
E = 2.828 RMS
sqrt 2 x E = 4 volts, peak
4 x 2 = 8 v P-P
3 db less is less voltage
-3 = 20 log (V2/8)
-3/20 = log (V2/8)
10^-3/20 = V2/8
8 x 10^(-3/20) = V2
5.66V p-p = V2

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11. ### J_Rod Thread Starter Member

Nov 4, 2014
109
6
Ah, okay, thanks for all the help. I have one more question... then 8V is the input voltage and 5.66V is the output voltage for the speaker?

12. ### #12 Expert

Nov 30, 2010
17,897
9,316
speakers do not, "output" voltage. They output sound.
8 volts is the peak to peak voltage for 1 watt of power into the speaker and 5.66 V P-P will get you 3db less loudness.

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13. ### WBahn Moderator

Mar 31, 2012
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One thing that seems to be a point of confusion for the TS is that dB is a measure of relative power. So when we talk about 70 dB of sound, we are talking about the amount of acoustic power in the sound relative to whatever was chosen as a reference for acoustic power. But when we talk about 10 dB with respect to an electrical signal, we are talking about the amount of electrical power relative to whatever was chosen as a reference for electrical power. The two references do not have to have anything to do with each other.

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14. ### Veracohr Well-Known Member

Jan 3, 2011
602
86
dB SPL? That's not exactly a 'comfortable' listening level in a room:

http://www.sengpielaudio.com/TableOfSoundPressureLevels.htm

Says a vacuum cleaner at 1m is 70dB and a busy street is 80dB SPL.

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15. ### #12 Expert

Nov 30, 2010
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Must be a really good vacuum cleaner.

I have a book that says 70db is, "conversational" level.
It was written by people that set up sound systems, so 70db might have been right for them.*
10dbSPL difference is "twice as loud" to the perception of a human, and I find 1000Hz rather irritating, so 60db would probably be the right answer for me.

* Sound System Engineering, Don and Carolyn Davis, page 25

Last edited: Feb 13, 2015
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Nov 4, 2014
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