Problem 13-32 Standing waves on string - Part 9 - B

The distance between nodes on a standing wave pattern on a certain string is \(16\; cm\) and there are 5 nodes between the ends of the string. A single wave takes \(1.2\; s\) to travel to one end of the rope and back again.

(a) What is the wavelength of the waves producing the pattern?
(b) How long is the rope?
(c) What is the speed of the waves?
(d) What is the frequency of the waves?
(e) What mode of vibration is occurring (i.e. which harmonic)?

Accumulated Solution

Diagram of harmonic wave.

\(\text{Internodal distance} = (1/2)\lambda \\ \lambda = 2 \times \text{internodal spacing} = 2 \times 16\; cm = 32\; cm \quad \text{(answer to part (a))} \\ \text{string length} = 3\lambda = 96 \;cm\; \text{(answer to part (b))} \\ v = d/t = (2 \times 96\; cm)/1.2\; s = 160 \;cm/s = 1.6\; m/s \quad \text{(answer to part (c))} \\ f = v/\lambda = (160\; cm/s)/(32\;cm) = 5.0\; s^{-1} \quad \text{(answer to part (d))}\)

Diagram of vibration.

added for each harmonic

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