Standing Waves Question

Question

Two waves are moving along a stretched string and in opposite directions have an amplitude of 4.0cm and a frequency of 14Hz at 8.4ms^-1.

a) If a standing wave were formed, how far apart would you expect the nodes to be from the antinodes on either side of them?

b) If the string had two fixed ends, what is the minimum length it must be in order for a standing wave to be possible?

Answer 1

For vibrating string

v = frequency*wavelength

8.4 = 14*wavelength

wavelength = 8.4/14 m=0.6m

Distance of node from anti node = wavelength/4

= 8.4/ (14*4) m =0.15m

Minimum length of string = wavelength / 2=8.4/28 m

=0.3m ( for one loop)

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