Answer to Question #286661 in Physics for Cathastrophy

Question

40. What is the velocity of the wave in a guitar string having a length of 0.65 m

and a mass of 3.5 g when subjected to a tension of 250 N?

41. While fishing, you notice that eight crests pass a given point in a time

interval of 10s. You approximate the distance between two crests to be 1.2

m. Calculate the

a) Speed of water waves and

b) Depth of water

42. On November 7, 1940, the Tacoma Narrows suspension bridge collapsed just

four months after it opened. Do research on causes why the bridge had set

in motion that led to its collapsed.

Answer 1

40)

$$v=\sqrt{\dfrac{T}{\mu}}=\sqrt{\dfrac{TL}{m}},$$ $$v=\sqrt{\dfrac{250\ N\times0.65\ m}{3.5\times10^{-3}\ kg}}=215.5\ \dfrac{m}{s}.$$

41)

a) Let's first find the period of the water waves:

$$T=\dfrac{seconds}{cycle}=\dfrac{10\ s}{8\ cycles}=1.25\ s.$$

Then, we can find the frequency of the water waves:

$$f=\dfrac{1}{T}=\dfrac{1}{1.25\ s}=0.8\ Hz.$$

Finally, we can find the speed of the water waves:

$$v=f\lambda=0.8\ Hz\times1.2\ m=0.96\ \dfrac{m}{s}.$$

b) Unfortunately, there is no data to answer this part of question.

42) The main reason is that engineers does not take into account the aerodynamic forces in the location of the bridge. As a result, Tacoma Narrows Bridge was collapsed due to vibrations that generated by the wind.