A string tied between two post is oscillating at 3Hz. A student determines the standing waves have a length of 4 meters. What is
1 answer:
Answer:
12 m/s
Explanation:
Standing waves are waves that are formed between two fixed points in space, so they cannot propagate, but they are just oscillations about a fixed points. Examples of standing waves are the waves in a string.
The relationship between wavelength, frequency and speed of a wave is given by the wave equation:
where
v is the speed of the wave
f is its frequency
is its wavelength
For the standing wave in this problem we have:
f = 3 Hz is the frequency of the wave
is the wavelength
Solving for v, we find the velocity of the wave:
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Answer:
A) K / K₀ = 4 b) v / v₀ = 4
Explanation:
A) For this exercise we can use the conservation of mechanical energy
in the problem it indicates that the displacement was doubled (x = 2xo)
starting point. At the position of maximum displacement
Em₀ = Ke = ½ k (2x₀)²
final point. In the equilibrium position
= K = ½ m v²
Em₀ = Em_{f}
½ k 4 x₀² = K
(½ K x₀²) = K₀
K = 4 K₀
K / K₀ = 4
B) the speed value
½ k 4 x₀² = ½ m v²
v = 4 (k / m) x₀
if we call
v₀ = k / m x₀
v = 4 v₀
v / v₀ = 4