You have two air columns that are each 2.210 m long. One column is open at both

Question

You have two air columns that are each 2.210 m long. One column is open at both ends and the other is closed at one end. You wish to determine the frequencies you can produce in the audible range (20 Hz–20,000 Hz) on a day when the temperature of the air is at 2.000°C. (Give your answers to at least four significant figures. Assume that the speed of sound at 0° C is exactly 331 m/s.)

(a) in the column that is open at both ends

(b) in the column that is closed at one end

Explanation / Answer

Given that :

length of column, L = 2.21 m

Assume, that the speed of sound at 0 0C, v = 331 m/s

(a) in the column that is open at both ends :

we know that, f = n (v / 2L)

At lowest frequency, we have

f1 = (1) [(331 m/s) / 2 (2.21 m)]

f1 = 74.8 Hz

At second lowest frequency, we have

f2 = (2) [(331 m/s) / 2 (2.21 m)]

f2 = 149.7 Hz

At highest frequency, we have

f3 = (3) [(331 m/s) / 2 (2.21 m)]

f3 = 224.6 Hz

(b) in the column that is closed at one ends :

we know that, f = n (v / 4L)

At lowest frequency, we have

f1 = (1) [(331 m/s) / 4 (2.21 m)]

f1 = 37.4 Hz

At second lowest frequency, we have

f2 = (2) [(331 m/s) / 4 (2.21 m)]

f2 = 74.8 Hz

At highest frequency, we have

f3 = (3) [(331 m/s) / 4 (2.21 m)]

f3 = 112.3 Hz

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