An ideal pendulum is often discussed when studying simple harmonic motion. What are the conditions needed for an ideal pendulum?
2 answers:
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Answer:
Speed = 209.5m/s
Direction = Positive x direction
Explanation:
The general wave equation expressing the displacement of a wave travelling in the positive x-direction is written as follows;
y(x, t) = y x cos(2kx - 2
ft) --------------------(i)
Where;
y(x, t) = the position of the wave at time t
y = the amplitude of the wave,
k = the wave number
f = frequency of the wave
Given;
y(x, t)= (3.0 cm) × cos(1.5x − 50t) -------------------(ii)
Comparing equations(i) and (ii)
=> y = amplitude
=> y = 3.0cm
=> y = 0.03m
Also,
=> 2kx = 1.5x
=> k =
=> wave number (k) =
Also,
=> 50t = 2ft
=> f = frequency
=> f = Hz
But,
=> wavelength (λ) = ------- (iii)
Substituting for k = in equation (iii)
=> λ = (2) ÷
=> λ = (2) x
(where
= 3.142)
=> λ = 26.33m
(a) To calculate the speed (v) of the wave, we use the formula;
v = f x λ
where f = and λ = 26.33
=> v = x 26.33
=> v = 209.5m/s
(b) To get the direction in which the wave is travelling, a quick look at the sign between the x and t terms (1.5x - 50t) in the given equation (ii) will suffice.
<em>A negative sign shows that the wave is travelling in the +x direction</em>
<em>A positive sign shows that the wave is travelling in the -x direction.</em>
In this case, the sign between these terms is negative. This shows that the wave is travelling in the positive x direction.