The concept needed to solve this problem is average power dissipated by a wave on a string. This expression ca be defined as

Here,
= Linear mass density of the string
Angular frequency of the wave on the string
A = Amplitude of the wave
v = Speed of the wave
At the same time each of this terms have its own definition, i.e,
Here T is the Period
For the linear mass density we have that

And the angular frequency can be written as

Replacing this terms and the first equation we have that



PART A ) Replacing our values here we have that


PART B) The new amplitude A' that is half ot the wavelength of the wave is


Replacing at the equation of power we have that


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Franklin had been waiting for an opportunity like this. He wanted to demonstrate the electrical nature of lightning, and to do so, he needed a thunderstorm.
He had his materials at the ready: a simple kite made with a large silk handkerchief, a hemp string, and a silk string. He also had a house key, a Leyden jar (a device that could store an electrical charge for later use), and a sharp length of wire. His son William assisted him.
Franklin had originally planned to conduct the experiment atop a Philadelphia church spire, according to his contemporary, British scientist Joseph Priestley (who, incidentally, is credited with discovering oxygen), but he changed his plans when he realized he could achieve the same goal by using a kite.
Answer:

Explanation:
given,
scattering angle of alpha particle = 25.0° above its initial direction of motion
oxygen nucleus recoils at = 50.0° below this initial direction.
final speed of the oxygen = 2.08×10⁵ m/s
mass of alpha particle = 4.0 u
mass o oxygen nucleus = 16 u
momentum conservation along x- axis


....(1)
Along y-direction




putting value in equation (1)

