Sample Essay On Lsp 121
Homework 7: Logs, Decibels and pH
Decibels are a measurement of sound intensity. The logarithmic relationship between intensity of a sound and sound level in decibels is given by the following formula:
L = 10 * log (I/Io)
L is the sound level in decibels, I is the intensity of the sound, and Io is the intensity of the softest sound that can be heard by humans.
I/Io is a ratio. This ratio is how many times louder a sound is than the softest audible sound. For this activity, we will only consider the ratio and not the individual pieces of the ratio.
Convert the above formula to exponent form. If you need help, remember to first divide both sides by 10. Then perform the same operation that we performed on Richter values to convert R = log (I) to 10R = I.
Solution: L/10 = log* (I/Io)
10^ (L/10) = 10^ [log* (I/Io)] = I/Io
Thus, I/Io = 10^ (L/10)
Open the decibels worksheet in the Logs.xls file. Using the formula above and the version from part a), fill in the empty cells with either the decibels or the ratios of the intensities. Copy and paste the table into your Word document.
What does it mean mathematically about the ratio of intensity for one sound to be 10 decibels louder than another sound?
Answer: L2 – L1 = 10 * log (I2/Io) - 10 * log (I1/Io)
L2 – L1 = 10 * log (I2/I1) = 10
Divide both sides by 10,
log (I2/I1) = 1
I2/I1 = 10
Thus, if sound 2 is 10 times louder than sound 1 in terms of decibels, the ratio of intensity of sound 1 is also 10 times greater than the intensity of sound 2.
The following statement is incorrect:
“A jet airplane landing at the local airport makes 120 decibels of noise. If we allow three jets to land at the same time, there will be 360 decibels of noise pollution.”
If one jet airplane makes 120 decibels of noise, what would the ratio of intensities be for one plane? What would the ratio of intensities be for all three planes? What would the decibel level be for the three jets? Is it 360 decibels as claimed above?
Answer: I/Io = 10^ (120/10) = 10^12. This is the value of the ratio of intensity for one plane only. Thus, the total ratio of intensities for all three planes is 3 x 10^12. The sound level L = 10* log (3x 10^12) = 124.77 ~ 125 dB. It is different from the 360 dB claimed above.
pH is the measure of the acidity or basicity of an aqueous solution. To the chemist, pH is a measure of the concentration of positive hydrogen ions, [H+], in a solution. The pH scale generally ranges from 1 to 14. Pure distilled water at 25˚C (about room temperature) is said to be neutral and has a pH of 7. Solutions with pH less than 7 are acidic and solutions with pH greater than 7 are basic. The relationship between pH and the hydrogen ion concentration is a logarithmic function with the following formula:
pH = -log([H+])
where [H+] is the symbol for hydrogen ion concentration.
.a) Convert the above formula to exponent form. If you need help, remember to first divide both sides by -1. Then perform the same operation that we performed above to remove the log function.
Solution: -pH = log([H+])
10^ (-pH) = [H+]
Thus, H+ concentration = [H+] = 10^ (-pH)
b) Open the pH worksheet in the Logs.xls file. Using the log formula above and the non-log version from part a), fill in the empty cells with either the pH or the [H+] values. Copy and paste the table into your Word document.
c) Borax, a cleaning agent, has a pH of 9.2. Is it basic or acidic? What is the [H+] concentration?
Answer: Borax is basic because its pH is greater than 14. The H+ concentration is [H+] = 10^ (-9.2) = 6.30 x 10^-10 moles / Liter.
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