Answer:
1. t = 0.0819s
2. W = 0.25N
3. n = 36
4. y(x , t)= Acos[172x + 2730t]
Explanation:
1) The given equation is

The relationship between velocity and propagation constant is

v = 15.87m/s
Time taken, 

t = 0.0819s
2)
The velocity of transverse wave is given by


mass of string is calculated thus
mg = 0.0125N

m = 0.00128kg


0.25N
3)
The propagation constant k is

hence

0.036 m
No of wavelengths, n is

n = 36
4)
The equation of wave travelling down the string is
![y(x, t)=Acos[kx -wt]\\\\becomes\\\\y(x , t)= Acos[(172 rad.m)x + (2730 rad.s)t]](https://tex.z-dn.net/?f=y%28x%2C%20t%29%3DAcos%5Bkx%20-wt%5D%5C%5C%5C%5Cbecomes%5C%5C%5C%5Cy%28x%20%2C%20t%29%3D%20Acos%5B%28172%20rad.m%29x%20%2B%20%282730%20rad.s%29t%5D)
![without, unit\\\\y(x , t)= Acos[172x + 2730t]](https://tex.z-dn.net/?f=without%2C%20unit%5C%5C%5C%5Cy%28x%20%2C%20t%29%3D%20Acos%5B172x%20%2B%202730t%5D)
Answer:
v = 2 v₁ v₂ / (v₁ + v₂)
Explanation:
The body travels the first half of the distance with velocity v₁. The time it takes is:
t₁ = (d/2) / v₁
t₁ = d / (2v₁)
Similarly, the body travels the second half with velocity v₂, so the time is:
t₂ = (d/2) / v₂
t₂ = d / (2v₂)
The average velocity is the total displacement over total time:
v = d / t
v = d / (t₁ + t₂)
v = d / (d / (2v₁) + d / (2v₂))
v = d / (d/2 (1/v₁ + 1/v₂))
v = 2 / (1/v₁ + 1/v₂)
v = 2 / ((v₁ + v₂) / (v₁ v₂))
v = 2 v₁ v₂ / (v₁ + v₂)
Answer:
The magnetic field is
Explanation:
From the question we are told that
The mass of the metal rod is 
The current on the rod is 
The distance of separation(equivalent to length of the rod ) is 
The coefficient of kinetic friction is 
The kinetic frictional force is 
The constant speed is 
Generally the magnetic force on the rod is mathematically represented as

For the rod to move with a constant velocity the magnetic force must be equal to the kinetic frictional force so

=> 
=> 
=> 