The tension in a string is 15 n, and its linear density is 0.85 kg/m. a wave on the string travels toward the −x direction; it has an amplitude of 3.6 cm and a frequency of 12 hz.
(a) what are speed and wavelength of the wave?
(a) write down the mathematical expression for the wave.

a) v = 4.20 m/s, 0.35 m

b) y = 0.036sin(24πt + 17.94x)

Explanation:

Given:

Tension in the string, T = 15 N

Linear density of the string, M = 0.85 kg/m

Amplitude of the wave, A = 3.6 cm = 0.036 m

Frequency of the wave, f = 12 Hz

a) now,

the speed (v) of the wave is given as:

v = √(T/M)

on substituting the values, we get

v = √(15/0.85)

or

v = 4.20 m/s

also, wavelength (λ) is given as:

λ = v/f

on substituting the values, we get

λ = 4.20/12

or

λ = 0.35 m

b) The mathematical expression for the wave is given as:

y = Asin(2πft + (2π/λ)x)

thus,

on substituting the values, we get

y = 0.036sin(2π×12×t + (2π/0.35)x)

or

y = 0.036sin(24πt + 17.94x)

the velocity you are looking for is made up of two parts: horizontally velocity, vh, and its vertical velocity, vv. the actual velocity of the ball will be these two parts added together, and because velocity is a vector then they will need to be added vectorially.  

neglecting air resistance etc etc.,  

the horizontal velocity component will be constant (because there is no accelerating force in the horizontal direction.  

vh = 8 ms-1  

the vertical velocity component has an accelerating force: 'g'.  

using v = u +at where a = g = 9.81 ms-2.  

the vertical component of velocity, vv = 0 + gt = vv =9.81 x 2  

vv = 19.62 ms-1 . the zero appears because the virtical component of velocity at time t=0 is zero. remember, the ball was thrown horizontally.  

how fast it will be moving (it actual path (being a parabola )) will be the vector sum of these two.  

adding vectorally gives: -  

v = sqr root (8^2 + 19.62^2) = sqr root(64+384.9) = 21.18 or 21.2 ms-1

in this image, you can see solar radiation going through ocean water.

no image, but probably absorption