The human eardrum has an area of 5.0×10–5 m2. (a) What is the sound power received when the incident intensity is the minimum perceivable, 1.0×10–12 W/m2? (b) What is the sound power at the eardrum for conversational speech, which has a sound level of 65 dB? (c) What is the sound power at the threshold of pain, 140 dB? answer to all parts in Watts pls. thanks

Question

The human eardrum has an area of 5.0×10–5 m2. (a) What is the sound power received when the incident intensity is the minimum perceivable, 1.0×10–12 W/m2? (b) What is the sound power at the eardrum for conversational speech, which has a sound level of 65 dB? (c) What is the sound power at the threshold of pain, 140 dB? answer to all parts in Watts pls. thanks

Answer 1

To find the sound power for each part of the question, we can use the formula:

Sound Intensity (I) = Power (P) / Area (A)

(a) To find the sound power received when the incident intensity is the minimum perceivable, we are given the minimum perceivable intensity (I = 1.0×10^(-12) W/m^2) and the area of the eardrum (A = 5.0×10^(-5) m^2).

Rearranging the formula, we can solve for power (P):

P = I * A

P = (1.0×10^(-12) W/m^2) * (5.0×10^(-5) m^2)

Calculating the result, we get:

P = 5.0×10^(-17) W

Therefore, the sound power received when the incident intensity is the minimum perceivable is 5.0×10^(-17) Watts.

(b) To find the sound power at the eardrum for conversational speech, which has a sound level of 65 dB, we need to convert dB to sound intensity.

Converting dB to intensity:

I = I0 * 10^(dB/10)

Where I0 is the reference intensity, which is usually 10^(-12) W/m^2.

Therefore, I = (10^(-12) W/m^2) * 10^(65/10)

Calculating the result, we get:

I = 10^(-10) W/m^2

Now, we can find the power (P) using the same formula as in part (a):

P = I * A

P = (10^(-10) W/m^2) * (5.0×10^(-5) m^2)

Calculating the result, we get:

P = 5.0×10^(-15) W

Therefore, the sound power at the eardrum for conversational speech is 5.0×10^(-15) Watts.

(c) To find the sound power at the threshold of pain, 140 dB, we follow the same steps as in part (b):

Converting dB to intensity:

I = I0 * 10^(dB/10)

I = (10^(-12) W/m^2) * 10^(140/10)

Calculating the result, we get:

I = 1.0 W/m^2

Now, we can find the power (P) using the same formula as before:

P = I * A

P = (1.0 W/m^2) * (5.0×10^(-5) m^2)

Calculating the result, we get:

P = 5.0×10^(-5) W

Therefore, the sound power at the threshold of pain is 5.0×10^(-5) Watts.