A sound wave of frequency 1310 Hz., propagating through air at 0 degrees Celsius, has a pressure amplitude of 11.0 Pa. What is the maximum particle speed (in meters/second)?
To find the maximum particle speed of a sound wave, we need to use the equation:
V = Aω
where:
V is the maximum particle speed,
A is the pressure amplitude,
and ω is the angular frequency.
The angular frequency (ω) can be calculated using the formula:
ω = 2πf
where:
ω is the angular frequency,
f is the frequency.
Now let's calculate the angular frequency:
ω = 2π × 1310 Hz
≈ 2π × 1310
≈ 2 × 3.14 × 1310
≈ 2 × 3.14 × 1310
≈ 8196.4 rad/s
Now that we have the angular frequency, we can calculate the maximum particle speed (V):
V = A × ω
= 11.0 Pa × 8196.4 rad/s
≈ 90160.4 m/s
Therefore, the maximum particle speed of the sound wave is approximately 90160.4 meters per second.