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?

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To find the amplitude of the pressure wave generated by the hair dryer, we can use the formula β = 20 log (P/P0), where β is the sound level in decibels and P is the pressure amplitude.

Given that β = 79 dB and P0 = 2.00·10^(-5) Pa, we need to rearrange the formula to solve for P:

β = 20 log (P/P0)
79 = 20 log (P/(2.00·10^(-5)))

Dividing both sides of the equation by 20:

log (P/(2.00·10^(-5))) = 79/20

Taking the antilog of both sides to remove the logarithm:

P/(2.00·10^(-5)) = 10^(79/20)

Multiplying both sides by 2.00·10^(-5):

P = (2.00·10^(-5)) * 10^(79/20)

Using a calculator to evaluate the expression:

P ≈ 0.1585 Pa

Therefore, the amplitude of the pressure wave generated by the hair dryer is approximately 0.1585 Pa.

To find the amplitude of the pressure wave generated by the hair dryer, we can use the formula β = 20 log (P/P0), where β is the sound level in decibels, P is the amplitude of the pressure wave, and P0 is the reference pressure.

Given that the sound level of the hair dryer is 79 dB, we substitute this value into the formula:

79 = 20 log (P/P0)

To find P, let's rearrange the equation:

log (P/P0) = 79/20

Now we need to express the equation in exponential form, so we take the antilog (inverse logarithm) of both sides:

P/P0 = 10^(79/20)

Next, we can multiply both sides of the equation by P0 to isolate P:

P = P0 * 10^(79/20)

Finally, we substitute the value of P0, which is 2.00·10^(-5) Pa, into the equation:

P = (2.00·10^(-5)) * 10^(79/20)

Calculating this expression will give us the amplitude of the pressure wave generated by the hair dryer.