What frequencies will a 150 m long tube produce in the audib

What frequencies will a 1.50 m long tube produce in the audible range (20 Hz - 20,000 Hz) at 15.0°C for the following cases? (a) the tube is closed at one end lowest frequency Hz second lowest frequency Hz highest frequency (rounded to the nearest Hz) (b) the tube is open at both ends lowest frequency Hz Hz second lowest frequency Hz highest frequency (rounded to the nearest Hz)

Solution

Speed of sound at T=15^oC

V=331+0.6*15 =340 m/s

a)

For tube is closed at on end ,frequency is given by

f_n=n(V/4L)

f_n=n(340/4*1.5) =n (56.67 Hz)

where n=1,3,5,-----352

Lowest frequency

f=56.67*1=56.67 Hz

Highest frequency

f=56.67*352 =19947 hz

b)

For tube is closed at both ends ,frequency is given by

f_n=n(V/2L)

f_n = n(340/2*1.5) =n(113,33 Hz)

where n=1,2,3,------------176

Lowest

f=113.33 Hz

Highest

f=176*113.33 =19947 hz