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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
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).
Following the previous pattern, next possible standing waves and its
lengths are:
http://newt.phys.unsw.edu.au/jw/fluteacoustics.html
Therefore,
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.
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
Flute has an open end and air is free to move. Pressure wave is
reflected with a phase change of pi.
CLARINET
Clarinet end is open but the mouthpiece is concealed by a reed.
Mouthpiece
covered by reed End is open
Clarinet has only one end open.
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.
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

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Standing waves on strings

  • 1.
  • 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:
  • 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.