standing waves on strings

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Standing waves on strings

Standing waves

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:

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

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

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 ropes 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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