Nevermind I figured it out. :)
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I believe that the speed will remain constant, and the new wavelength will be half of the original wavelength. Speed = (frequency) x (wavelength). This depends on the method used to increase the frequency. If the tension on the string is increased while maintaining the same length (like tuning up a guitar string), then the speed will increase, rather than the wavelength.
For a pendulum, or a child on a swing: Change the length of the pendulum or the swing-chains. For a guitar string: Change the tension (tune it), or the length (squeeze it into a fret). For an electronic oscillator: Change the piezo crystal, or change a capacitor or inductor for one of a different value.
no idea
Tension rods are mainly found in places such as the bathroom or the closet. Tension rods are useful for providing a place for something, like a curtain, to hang from without drilling holes into a wall.
There are two forces acting on the bucket which are the Tension and the Weight. Tension is directed upward and Weight is directed downward. Since the bucket is either moving at constant velocity, or if its remaining still, the Tension would have to equal in magnitude to the weight. Weight = Fg = Mass(in kgs) times Gravity= 4.2 kg x 9.8 m/s^2=41.46 Newtons Tension would be equal to Fg, which means that Tension would also be 41.46 Newtons.