Question

An instructor gives a demonstration in which he makes a standing wave on a long thin slinky. The slinky is 6.0 meters long. If you see 3 loops on the slinky when the instructor shakes the end of the slinky at a rate of 2.50 cycles per second, then the speed (in m/s) of transverse traveling waves on the slinky is

Answer 1

The characteristics of standing waves allows to find the result for the speed of the wave is:

• The speed wave is:  v = 10 m / s

The wave is a way of transmitting energy without mass displacement, , in the attachment we can see a diagram of the standing wave.

Each cycle corresponds to half a wavelength,  they indicate that the frequency is 2.50 Hz and there are three cycles, so the wavelength is:

      L = $n \frac{\lambda}{2}$

      λ = 2L/n

      λ = 2 6 /3

       λ = 4 m

Wave speed is related to wavelength and frequency

        v = λ f

         v = 4 2.5

         v = 10 m / s

In conclusion, using the characteristics of standing waves we can find the result for the speed of the wave is:

• The wave speed is:   v = 10 m / s

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