Which of the following is an accurate statement? A) Standing waves can be set up

Question

Which of the following is an accurate statement?
A) Standing waves can be set up in a pipe closed on both ends, but not in one with one end
open and one end closed.
B) The fundamental frequency of an organ pipe is determined primarily by the pipe
diameter.
C) The open end of a pipe is a pressure antinode for standing waves.
D) Displacement nodes and pressure antinodes occur at the same place in an organ pipe.
E) Standing sound waves can be set up in a pipe open on one end, but not on one open on
both ends.

I know the answer is D but can anyone explain why? I would also like to know what the wrong answers are wrong. Any assistance would be greatly appreciated.

Explanation / Answer

The simplest pattern along the string is a single antinode in the centre. As this node-antinode-node forms half a sine wave, the physical length l of the string equals half a wavelength (?1) of this bottom frequency, f1. as f = v / ? , f1 = v /?1 = v /2l thus f1 = (T/µ)1/2 / 2l This frequency is known as either the FUNDAMENTAL or the FIRST HARMONIC. The next pattern has a whole standing wave along the string. For the same string, the wavelength ?2 is now equal to the length, ?2 = l , so f2 = 2 x (T/µ)1/2 / 2l This is the first complication so it is called the FIRST OVERTONE and as the frequency is twice the simplest it is also called the SECOND HARMONIC. Similarly, the SECOND OVERTONE has a frequency of thrice the simplest so is the THIRD HARMONIC. Generally, fn = v /?n = nv /2l = n(T/µ)1/2 / 2l

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