standing waves on strings
Post on 17-Jul-2015
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Standing waves on strings
By Sun Ah Jo
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:
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:
Lets look at flute and clarinet to have a better understanding of standing waves. Both of these instruments create sound through vibrating air column.
Flute is open at both ends meaning that both ends are non-fixed ends (pressure is close to atmospheric).
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 end is open but the mouthpiece is concealed by a reed.
Mouthpiece covered by reed
End is open
Clarinet has only one end open.
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 ropes linear density as 8.0g/m.