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

przesypkai4

Answered question

2022-07-15

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?

Answer & Explanation

palatinizi

palatinizi

Beginner2022-07-16Added 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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