The sound level in decibels is typically expressed as β = 10 log (I/I0), but since sound is a pressure wave, the sound level can be expressed in terms of a pressure difference. Intensity depends on the amplitude squared, so the expression is β = 20 log (P/P0), where P0 is the smallest pressure difference noticeable by the ear: P0 = 2.00·10-5 Pa. A hair dryer has a sound level of 79 dB, find the amplitude of the pressure wave generated by this hair dryer

Question

The sound level in decibels is typically expressed as β = 10 log (I/I0), but since sound is a pressure wave, the sound level can be expressed in terms of a pressure difference. Intensity depends on the amplitude squared, so the expression is β = 20 log (P/P0), where P0 is the smallest pressure difference noticeable by the ear: P0 = 2.00·10-5 Pa. A hair dryer has a sound level of 79 dB, find the amplitude of the pressure wave generated by this hair dryer

Answer 1

20Log(P/Po) = 79db,

Divide both sides by 20:
Log(P/Po) = 3.95,
P/Po = 10^3.95,
Multiply both sides by Po:
P = 10^3.95 * Po,
P = 1*10^3.95 * 2*10^-5,
P = 2*10^-1.05 = 0.1783.

Answer 2

To find the amplitude of the pressure wave generated by the hair dryer, we'll use the formula:

β = 20 log (P/P0)

We know that the sound level (β) of the hair dryer is 79 dB. So we can substitute this value in the formula:

79 = 20 log (P/P0)

To find P, we need to rearrange the formula:

P/P0 = 10^(β/20)

Now, we can substitute the known values:

P/P0 = 10^(79/20)

P/P0 = 10^3.95

P/P0 ≈ 7943.28

Now, we can solve for P by multiplying both sides of the equation by P0:

P = P0 * (10^(β/20))

Substituting the value of P0:

P ≈ (2.00·10^-5) * (10^(79/20))

P ≈ 6.32 * 10^-2 Pa

Therefore, the amplitude of the pressure wave generated by the hair dryer is approximately 6.32 * 10^-2 Pa.