Answer:
1.3964m
Step-by-step explanation:
When a closed pipe (one end open and one end closed) is set to vibrate, standing waves can form inside it. These standing waves have specific frequencies at which they can vibrate, called resonant frequencies. The fundamental frequency is the lowest resonant frequency of the pipe, and it depends on the length of the pipe.
The formula for the fundamental frequency of a closed pipe is:
f = (n v) / (2 L)
where f is the fundamental frequency, n is an integer (1, 2, 3, etc.) representing the number of half-wavelengths in the air column, v is the speed of sound in air at the given temperature, and L is the length of the air column.
To solve this problem, we are given the fundamental frequency (125 Hz) and the air temperature (30°C), and we need to find the corrected length of the air column. We can rearrange the formula above to solve for L:
L = (n v) / (2 f)
We are given that the pipe is resonant at the fundamental frequency, which means that n = 1. We also need to find the speed of sound in air at 30°C. The formula for the speed of sound in air at a given temperature is:
v = 331.5 + 0.6 T
where T is the temperature in degrees Celsius. Substituting T = 30°C, we get:
v = 331.5 + 0.6 x 30 = 349.5 m/s
Now we can substitute the values we have into the formula for L:
L = (1 x 349.5) / (2 x 125) = 1.397 m
Rounding to two significant figures, we get the corrected length of the air column in a closed pipe resonant at a fundamental frequency of 125 Hz and air temperature of 30°C to be approximately 1.40 m.