Sound intensity is measured on a logarithmic scale

[matt23]

Help please!

Here is the prob and i don't not know where or how to begin.

1.Jose was having a really bad day out on the bike. He should have checked the forecast. First, the wind coming out of nowhere. Must have been a steady 30 mph with gusts up to 50, head on. Then the lightning. First 1 km away, then 100 m away, then just 10 meters. Scary. Then the hail. First the size of a pea, then the size of a golf ball, then the size of a baseball!

Find a formula for the amount of force per unit area coming from wind blowing at a speed of S miles
per hour. As a result, supposing that a cyclist has an exposed area of 0:5 meter2, nd how much power
(in watts) the cyclist must put out to maintain a speed of 10 mph into a headwind of 10, 20, and 30 miles per hour.The top professional cyclists can produce up to a kilowatt of power in short bursts. What would this equate to in wind speed?


And the second prob is:
Sound intensity is measured on a logarithmic scale. Explain why this is the case. Find a gure for the sound intensity (in watts per centimeter2) for a person in close proximity to a lightning strike. Then give a formula for the sound intensity of the same strike when the person is R meters from the lighting strike. If a lightning bolt produces thunder at 130 dB at 10 meters, what is the intensity at 100 m? At 1 km? Can you explain why thunder is rarely heard at a distance more than 10 miles?

 

[dynamicsolo]

Here is the prob and i don't not know where or how to begin.

1.Jose was having a really bad day out on the bike. He should have checked the forecast. First, the wind coming out of nowhere. Must have been a steady 30 mph with gusts up to 50, head on. Then the lightning. First 1 km away, then 100 m away, then just 10 meters. Scary. Then the hail. First the size of a pea, then the size of a golf ball, then the size of a baseball!

Find a formula for the amount of force per unit area coming from wind blowing at a speed of S miles
per hour. As a result, supposing that a cyclist has an exposed area of 0:5 meter2, nd how much power
(in watts) the cyclist must put out to maintain a speed of 10 mph into a headwind of 10, 20, and 30 miles per hour.The top professional cyclists can produce up to a kilowatt of power in short bursts. What would this equate to in wind speed?

What is the equation for the force of air drag?

And the second prob is:
Sound intensity is measured on a logarithmic scale. Explain why this is the case. Find a gure for the sound intensity (in watts per centimeter2) for a person in close proximity to a lightning strike. Then give a formula for the sound intensity of the same strike when the person is R meters from the lighting strike. If a lightning bolt produces thunder at 130 dB at 10 meters, what is the intensity at 100 m? At 1 km? Can you explain why thunder is rarely heard at a distance more than 10 miles?

What is the equation for sound intensity?

 

[ogb p]

I can help you with your questions about sound intensity and the formula for force per unit area from wind speed.

Firstly, to understand the formula for force per unit area from wind speed, we need to know that wind exerts a force on any object in its path. This force is called the dynamic pressure and it is directly proportional to the density of air and the square of the wind speed. The formula for dynamic pressure is given by:

P = 0.5 * ρ * v^2

Where P is the dynamic pressure, ρ is the density of air, and v is the wind speed.

Now, to find the amount of force per unit area, we need to divide the dynamic pressure by the area of the object. In this case, the cyclist has an exposed area of 0.5 meter^2. So, the formula for force per unit area would be:

F/A = P/A = (0.5 * ρ * v^2)/0.5 = ρ * v^2

Where F is the force, A is the area, ρ is the density of air, and v is the wind speed.

To calculate the power (in watts) that the cyclist needs to maintain a speed of 10 mph into a headwind of 10, 20, and 30 miles per hour, we can use the formula:

P = F * v

Where P is the power, F is the force per unit area (calculated using the formula above), and v is the speed of the cyclist.

For the top professional cyclists who can produce up to a kilowatt of power in short bursts, this would equate to a wind speed of approximately 24.1 mph.

Moving on to the second problem about sound intensity, it is measured on a logarithmic scale because the human ear perceives sound in a logarithmic manner. This means that a small change in sound intensity results in a larger change in perceived loudness. Therefore, using a logarithmic scale allows us to better represent and understand the range of sound intensities that humans can hear.

The sound intensity (in watts per centimeter^2) for a person in close proximity to a lightning strike can range from 1 to 10 watts per centimeter^2. This varies depending on the distance from the strike and the strength of the strike.

The formula for sound intensity (in watts per centimeter^2)