A concert loudspeaker suspended high off the ground emits 35 W of sound power. A small
microphone with a 1.0 cm2 area is 50 m from the speaker.
(a) What is the sound intensity at the position of the microphone?
(b) How much sound energy impinges on the microphone each second?
To solve this problem, we need to use the formulas for sound intensity and sound energy.
(a) The sound intensity (I) is defined as the sound power (P) divided by the area (A) over which the sound spreads. The formula for sound intensity is:
I = P / A
Given:
Sound power (P) = 35 W
Area (A) = 1.0 cm2 = 1.0 x 10^-4 m2
Substituting these values into the formula:
I = 35 W / 1.0 x 10^-4 m2
I = 3.5 x 10^5 W/m^2
Therefore, the sound intensity at the position of the microphone is 3.5 x 10^5 W/m^2.
(b) The sound energy impinging on the microphone each second can be calculated by multiplying the sound intensity by the area of the microphone. The formula for sound energy (E) is:
E = I x A
Given:
Sound intensity (I) = 3.5 x 10^5 W/m^2
Area (A) = 1.0 cm2 = 1.0 x 10^-4 m2
Substituting these values into the formula:
E = (3.5 x 10^5 W/m^2) x (1.0 x 10^-4 m2)
E = 3.5 x 10^1 J/s
Therefore, the sound energy impinging on the microphone each second is 3.5 x 10^1 J/s.
To find the sound intensity at the position of the microphone, we can use the formula:
Sound Intensity (I) = Power (P) / Area (A)
(a) First, let's calculate the sound intensity:
Given:
Power of the speaker, P = 35 W
Area of the microphone, A = 1.0 cm² = 1.0 × 10⁻⁴ m²
Using the formula: I = P / A
I = 35 W / (1.0 × 10⁻⁴ m²)
Now, let's do the calculation:
I = 35 W / 1.0 × 10⁻⁴ m²
I = 35 × 10⁴ W/m²
I = 3.5 × 10⁵ W/m²
So, the sound intensity at the position of the microphone is 3.5 × 10⁵ W/m².
(b) To calculate the amount of sound energy impinging on the microphone per second, we can use the formula:
Sound energy (E) = Power (P) × Time (t)
Given:
Power of the speaker, P = 35 W (already given)
Time, t = 1 second (as we are calculating per second)
Using the formula: E = P × t
E = 35 W × 1 second
E = 35 Joules
So, the sound energy impinging on the microphone each second is 35 Joules.
a) is a standard formula
b) what is the surface area at 50m
Area= 4PI(50)^2
area of mike= 1cm^2*=(1m/100cm)^2=1E-4m^2
sound energy=35*1E-4/4PI2500