Intensity of 4Mhz in 1.54mm = 2W/cm2
at 4cm intensity =?
I know the answer is 0.32, but I do not understand why. Can you please explain?
I did figure out that Attenuation= 8db.
4/2 x 4cm = 8db.
Thank you in advance. I appreciate it!
To understand why the intensity at 4 cm is 0.32 W/cm², we need to consider the concept of attenuation and the inverse square law for intensity.
Attenuation:
The attenuation value of 8 dB indicates a reduction in intensity. The decibel (dB) is a logarithmic unit used to compare the relative power levels of two signals. In the case of attenuation, it represents a decrease in power.
The formula to convert dB to the attenuation factor (AF) is:
AF = 10^(-attenuation/10)
Here, the attenuation value is 8 dB:
AF = 10^(-8/10)
AF = 10^(-0.8)
AF = 0.15849
The attenuation factor tells us that the intensity at 4 cm is approximately 0.15849 times the intensity at 1.54 mm.
Inverse Square Law:
The inverse square law states that the intensity of a wave decreases as the square of the distance from the source increases. Mathematically, it can be expressed as:
I₂ = I₁ / (r₂ / r₁)²
Let's plug in the given values:
I₁ = 2 W/cm² (intensity at 1.54 mm)
r₁ = 1.54 mm = 0.154 cm (distance at 1.54 mm)
r₂ = 4 cm (distance at 4 cm)
Now, let's calculate I₂:
I₂ = I₁ / (r₂ / r₁)²
I₂ = 2 / (4 / 0.154)²
I₂ = 2 / (25.974)²
I₂ = 2 / 675.126276
I₂ = 0.0029627 W/cm²
Therefore, the intensity at 4 cm is approximately 0.0029627 W/cm².
To convert this value to scientific notation, we can write it as 2.9627 × 10^(-3) W/cm².
If you performed further calculations and found that the answer is 0.32, there might be an error in the calculations or a rounding discrepancy. The correct value, according to the given information, is 0.0029627 W/cm².