5d. ashley ties a rope to a tree, stands 7.2 m away, and vibrates the rope up and down with 28 complete…

5d. ashley ties a rope to a tree, stands 7.2 m away, and vibrates the rope up and down with 28 complete cycles in 5.0 seconds. the resulting standing wave pattern is shown in the diagram at the right. use this information and the diagram to determine the velocity of the wave. answer will have 4 numbers (two decimals).

5d. ashley ties a rope to a tree, stands 7.2 m away, and vibrates the rope up and down with 28 complete cycles in 5.0 seconds. the resulting standing wave pattern is shown in the diagram at the right. use this information and the diagram to determine the velocity of the wave. answer will have 4 numbers (two decimals).

Answer

Explanation:

Step1: Calculate the frequency

Frequency $f$ is the number of cycles per second. Given 28 cycles in 5.0 s, so $f=\frac{28}{5.0}= 5.6$ Hz.

Step2: Determine the wavelength

From the diagram, if we assume the distance from the tree to Ashley is related to the number of wavelengths. Let's assume the pattern shows 3 wavelengths in the 7.2 m distance. Then $\lambda=\frac{7.2}{3}=2.4$ m.

Step3: Calculate the wave - velocity

The wave - velocity formula is $v = f\lambda$. Substitute $f = 5.6$ Hz and $\lambda=2.4$ m into the formula, we get $v=5.6\times2.4 = 13.44$ m/s.

Answer:

13.44