You have two air columns that are each 2.310 m long. One column is open at both

Question

You have two air columns that are each 2.310 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-200009 Hz) on a day when the temperature of the air is at 22.00 degree C. (Give your answer to at least four significant figures. Assume that speed of sound at 0 degree C is exactly 331 m/s.) in the column that is open at both ends lowest frequency Hz second lowest frequency Hz Highest frequency Hz in the column that is closed at both ends lowest frequency Hz second lowest frequency Hz Highest frequency Hz

Explanation / Answer

a) lowest frequency = f1= nv/2L = (1*343)/(2*2.310) = 37.12 Hz

Second lowest frequency = 2f1= nv/4L = (2*343)/(2*2.310) = 2*37.12 m/s = 74.24 Hz

Highest frequency will be at n= 538

Hence f(highest) = nv/4L = (269*343)/(4*2.310) = 538*37.12 = 19970.56 Hz

b) lowest frequency = f1= nv/4L = (1*343)/(4*2.310) = 74.24 Hz

Second lowest frequency = 2f1= nv/4L = (2*343)/(4*2.310) = 2*74.24m/s = 148.48 Hz

Highest frequency will be at n= 269

Hence f(highest) = nv/4L = (269*343)/(4*2.310) = 269*74.24 = 19970.56 Hz

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