A standing wave is a vibrational pattern formed within a medium when reflected and incident waves interfere. The document discusses the behavior of standing waves in musical instruments like flutes and clarinets, explaining their different configurations and how air columns vibrate to produce sound. Additionally, it presents a problem involving the frequency of a vibrating rope with specific parameters.

2. Standing wave is a “vibrational pattern created within a medium when
the vibrational frequency of the source causes reflected waves from
one end of the medium to interfere wit incident waves from the source.”
Equations used are as the following:
STANDING WAVE

3. STRING FIXED AT BOTH ENDS
Consider a string of length L with both ends fixed. This image below
demonstrates only half of its wavelength meaning that:
*note: ‘N’ stands for node (point of no displacement) and ‘A’
stands for antinode (point of maximum amplitude).

4. Following the previous pattern, next possible standing waves and its
lengths are:

5. http://newt.phys.unsw.edu.au/jw/fluteacoustics.html
Therefore,

6. INSTRUMENTS
Let’s look at flute and clarinet to have a better understanding of standing
waves. Both of these instruments create sound through vibrating air
column.

7. FLUTE
Flute is open at both ends meaning that both ends are non-fixed ends
(pressure is close to atmospheric).
Mouthpice open End of foot joint open

8. Flute has an open end and air is free to move. Pressure wave is
reflected with a phase change of pi.

9. CLARINET
Clarinet end is open but the mouthpiece is concealed by a reed.
Mouthpiece
covered by reed End is open

10. Clarinet has only one end open.

11. QUESTION
In a playground, a swing has a rope density of 1400kg/m^3 and diameter
of 0.8cm. While Jimmy was running to ride the see-saw, he slightly
brushed the 1.50m long rope, which has a tension of 10N, causing the
rope to vibrate. With what frequency will the rope vibrate? Assume the
rope’s linear density as 8.0g/m.

12. 1400kg/m^3
0.8cm=0.008m
1.50m
10N
0.008kg/m
10N
0.008kg/m = 35.36m/s
35.36m/s
3m
11.79 Hz
SOLUTION