Answer:
mantle convection is the very slow creeping motion of earths solid silicate mantle caused by convection currents carrying heat from the interior to the planet's surface.
Answer:
0.6983 m/s
Explanation:
k = spring constant of the spring = 0.4 N/m
L₀ = Initial length = 11 cm = 0.11 m
L = Final length = 27 cm = 0.27 m
x = stretch in the spring = L - L₀ = 0.27 - 0.11 = 0.16 m
m = mass of the mass attached = 0.021 kg
v = speed of the mass
Using conservation of energy
Kinetic energy of mass = Spring potential energy
(0.5) m v² = (0.5) k x²
m v² = k x²
(0.021) v² = (0.4) (0.16)²
v = 0.6983 m/s
To verify the identity, we can make use of the basic trigonometric identities:
cot θ = cos θ / sin θ
sec θ = 1 / cos <span>θ
csc </span>θ = 1 / sin θ<span>
Using these identities:
</span>cot θ ∙ sec θ = (cos θ / sin θ ) (<span> 1 / cos </span><span>θ)
</span>
We can cancel out cos <span>θ, leaving us with
</span>cot θ ∙ sec θ = 1 / sin θ
cot θ ∙ sec θ = = csc <span>θ</span>
To develop this problem it is necessary to apply the oscillation frequency-related concepts specifically in string or pipe close at both ends or open at both ends.
By definition the oscillation frequency is defined as

Where
v = speed of sound
L = Length of the pipe
n = any integer which represent the number of repetition of the spectrum (n)1,2,3...)(Number of harmonic)
Re-arrange to find L,

The radius between the two frequencies would be 4 to 5,


Therefore the frequencies are in the ratio of natural numbers. That is

Here f represents the fundamental frequency.
Now using the expression to calculate the Length we have

Therefore the length of the pipe is 1.3m
For the second harmonic n=2, then

Therefore the length of the pipe in the second harmonic is 2.6m