| Date | November 2011 | Marks available | 3 | Reference code | 11N.3.SL.TZ0.2 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 0 |
| Command term | Show that | Question number | 2 | Adapted from | N/A |
Question
This question is about standing waves in an organ pipe.
The diagram shows an organ pipe that is open at both ends.
The pipe is emitting its lowest frequency note.
On the diagram above,
(i) sketch a representation of the standing wave set up in the pipe.
(ii) label with the letter P, the point or points within the pipe where the air pressure is a maximum.
(iii) label with the letter A, the displacement antinodes.
The length of the pipe in (a) is 1.5 m. An organ pipe that is closed at one end has the same lowest frequency note as the pipe in (a).
Show that the length of this pipe is 0.75 m.
Markscheme
(i) waveform showing node at centre and antinodes at end;
(ii) P as shown;
(iii) A as shown;
for open pipe \(f = \frac{v}{{2l}}\left( { = \frac{v}{{3.0}}} \right)\);
for closed pipe \(f = \frac{v}{{4l}} = \frac{v}{{3.0}}\);
so l = 0.75m
