Sound pressure level L in decibels is given by L=20log p/p_0 , where p is the sound pressure and p_0 is a reference pressure. The sound pressure level of a jet engine is 145 decibels, when p_0 is the sound pressure at the threshold of hearing, 2×10^−5 pascal. a. Write and solve an equation to find the sound pressure p of the jet engine to the nearest pascal. b. How many times the sound pressure at the threshold of hearing is the sound pressure of the jet engine?

przesypkai4 2022-07-15 Answered
Sound pressure level L in decibels is given by L = 20 l o g p p 0 , where p is the sound pressure and p 0 is a reference pressure. The sound pressure level of a jet engine is 145 decibels, when p 0 is the sound pressure at the threshold of hearing, 2 × 10 5 pascal. a. Write and solve an equation to find the sound pressure p of the jet engine to the nearest pascal. b. How many times the sound pressure at the threshold of hearing is the sound pressure of the jet engine?
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Answers (1)

palatinizi
Answered 2022-07-16 Author has 3 answers
a) We let L = 145 , p 0 = 2 × 10 5 in the formula given:
145 = 20 log p 2 × 10 5
Divide both sides by 20:
7.25 = log p 2 × 10 5
Rewrite in exponential form:
10 7.25 = p 2 × 10 5
Solve for p:
p = 10 7.25 2 × 10 5
=356Pa
b) This is given by the ratio p p 0 :
p p 0 = 356 2 × 10 5 = 17 , 800 , 000
Result:
a.356 Pascal
b. 17,8000,000 times greater

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