Question

The loudest animal on Earth is the blue whale. Blue whales can emit sound with an intensity of 106.8 watts/met er². The equation beta =10log (frac II_0) relates the sound level, β, in decibels (dB), of a noise with an intensity of / to the smallest sound intensity that can be hea by the human ear, I_0 (approximately 1* 10⁻¹² watts/me er²) Based on this information, which value is closest to the sound level, in decibels, of the vocalizations of a blue whale?

A. 240 dB
B. 1,000 dB
C. 100 dB
D. 140 dB

Answer 1

The sound level of blue whale vocalizations, calculated using the provided intensity and the reference intensity, is just under 190 dB. Since this exact value is not a choice and the closest option should not exceed our result, the closest provided choice is 140 dB. Option D is correct.

Step-by-step explanation:

To find the sound level in decibels (dB) for the vocalizations of a blue whale, we use the equation ß = 10 log (I / I_0), where ß is the sound level in decibels, I is the sound intensity, and I_0 is the reference intensity of 1 x 10⁻¹² watts per meter squared (W/m²) - the smallest sound intensity that can be heard by the human ear. Given that the intensity of blue whale vocalizations is 106.8 W/m², we can calculate the sound level as follows:

ß = 10 log (106.8 / 1 x 10⁻¹²) = 10 log (106.8 x 10¹²) = 10 log (10¹´¸¸) ≈ 10 x 18.8 = 188 dB

The calculated value falls just under 190 dB, which means the closest value from the choices provided would be 190 dB; however, since 190 dB is not an option and the actual value is not exactly 190 dB, the closest provided option that does not exceed the calculated value is D. 140 dB.