A loud speaker inside a room is generating sound that spreads out uniformly in all directions. At a certain location 5 m away from the loud speaker, the sound waves coming directly from the speaker (without reflecting from the walls) create a decibel level of 75.0 dB with respect to the threshold of hearing. (a) What is the power of the loud speaker

Explanation:

We shall convert decibel into intensity of sound in Watt / m²

75 decibell = 7.5 bell

7.5 = log ( I / 10⁻¹² )

I / 10⁻¹² = 10⁷°⁵

I = 10⁻¹² x  10⁷°⁵

= 10⁻⁴°⁵ watt / m²

Let power of the loudspeaker be P

intensity of sound 5m away will be given by the formula

P / 4π d² where , d is distance of the point at which intensity is measured

Puting the given values

P /4π 5² = 10⁻⁴°⁵

P = 4π 5² x 10⁻⁴°⁵

= 99.3 x 10⁻⁴ W

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2