I can never remember what is the lowest (fundamental) frequency of a closed air column. So I went and looked it up just now ... thank you.
The fundamental (lowest frequency, longest wavelength) of an air column that's closed at one end is a wavelength that's four times the length of the air column. I think that's all we need to answer both of these questions.
Question #3: How long is the length of the tube, closed at one end ? Given info: Speed of sound = 344 m/s, fundamental frequency = 220 Hz.
Wavelength = (speed) / (frequency) = (344 m/s) / (220 Hz) = 1.564 meters
In a pipe with one end closed, this is 4 times the length of the pipe. So the length of the pipe is (1/4)(1.564 m) = 0.391 meter. Is this one of the choices ? Well by golly, zounds, and blow me down, it is ! It's the last choice !
Question #4: What's the fundamental frequency of the tube, closed at one end ? Given info: Speed of sound = 344 m/s. Length of the tube: This isn't completely clear the way that 2nd sentence is worded. Are we working with an air column that's 14cm long (tube empty) or 7cm long (tube half full of water) ? Well, it does say the words "the length of the air column in the tube is 14cm", so let's work it that way and see what happens.
Fundamental wavelength = 4 x air column = 56 cm.
Frequency = speed/wavelength = (344 m/s) / (0.56 m) = 614 Hz. Is this one of the choices ? Non monsieur.
So let's try it with the tube half full of water ... air column 7cm long.
Wavelength = 4 x air column = 28cm
Frequency = speed/wavelength = (344 m/s) / (0.28 m) = 1229 Hz. Is this one of the choices ? 1230 Hz is ! Blimey ! This must be it ! The question is worded in a confusing way, but it's trying to tell us that you take a 14cm test tube, fill it halfway up with water, and THEN blow across it to make it whistle.
Question #5: What is the frequency ? Given info: 4.88m pipe closed at one end. Use speed of sound = 344 m/s.
Fundamental wavelength = 4 x air column = 19.52 meters
Frequency = speed/wavelength = (344 m/s) / (19.52m) = 17.6 Hz.
This is one of those notes that the organist plays with the foot-pedals under his bench. Technically, the audience can't actually 'hear' that note with their ears. It's one of the notes that makes the whole concert hall pulsate. It's thrilling if you're in the live audience. If you're not, it takes a good music system and expensive speakers to reproduce that note, make your living room shake, and bring the neighbors out to threaten you with bodily harm if you don't turn it down. The finale of the Saint Saëns Symphony #3, in C Minor, Opus 78, the "Organ Symphony", is a great example.