To calculate the length of the air column needed to hear the third harmonic of a standing sound wave in an air column closed at one end, we can use the formula:
L = (4/n) * v / f
Where: L is the length of the air column n is the harmonic number v is the speed of sound in air f is the frequency of the sound wave
Given: Temperature (T) = 25°C Frequency (f) = 340 Hz Harmonic number (n) = 3
We need to determine the speed of sound in air at 25°C. The speed of sound in air can be approximated using the formula:
v = 331.4 + 0.6 * T
Substituting the given temperature value: v = 331.4 + 0.6 * 25 v ≈ 331.4 + 15 v ≈ 346.4 m/s
Now, we can calculate the length of the air column using the formula:
L = (4/n) * v / f L = (4/3) * 346.4 / 340 L ≈ 4.515 m
Therefore, to hear the third harmonic in an air column closed at one end, the length of the air column should be approximately 4.515 meters.