What is the relationship between electrostatic force and electric field?
1 answer:
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Corrected and Formatted Question:
A wave on a string is described by y(x, t) = (3.0 cm) × cos[2π(x/(2.4 m) + t/(0.20 s))], where x is in m and t in s.
(a) In what direction is this wave traveling?
(b) What are the wave speed, frequency, and wavelength?
(c) At t = 0.50 , what is the displacement of the string at x = 0.20 m?
Answer:
The wave is travelling in the negative x direction
The wave speed = 12.0m/s
The frequency = 5Hz
The wavelength = 2.4m
The displacement at t = 0.50s and x = 0.20m is -0.029m
Explanation:
The general wave equation is given by;
y(x, t) = y cos (2(x/λ) - 2
ft) --------------------------------(i)
Where;
y(x, t) is the displacement of the wave at position x and a given time t
y = amplitude of the wave
f = frequency of the wave
λ = wavelength of the wave
Given;
y(x, t) = (3.0 cm) × cos[2π(x/(2.4 m) + t/(0.20 s))] ------------------(ii)
Which can be re-written as;
y(x, t) = (3.0 cm) × cos[2π(x/(2.4 m)) + 2π(t/(0.20 s))] -------------(iii)
Comparing equations (i) and (iii) we have that;
=> 2π(x/(2.4 m) = 2π(x/λ)
=> λ = 2.4m
Therefore the wavelength of the wave is 2.4m
Also, still comparing the two equations;
=> 2π(t/(0.20 s) = 2πft
=> f = 1 / 0.20
=> f = 5Hz
Therefore the frequency of the wave is 5Hz
To get the wave speed (v), it is given by;
v = f x λ
Where f = 5Hz and λ = 2.4m
=> v = 5 x 2.4
=> v = 12.0m/s
Therefore, the speed of the wave is 12.0m/s
At t = 0.50s and x = 0.20m;
The displacement, y(x,t) of the string wave is given by
y(x, t) = (3.0 cm) × cos[2π(x/(2.4 m) + t/(0.20 s))]
<em>Convert the amplitude of 3.0cm to m</em>
=> 3.0cm = 0.03m
<em>Substitute this back into the equation</em>
=> y(x, t) = (0.03m) × cos[2π(x/(2.4 m) + t/(0.20 s))]
<em>Substitute the values of t and x into the equation above;</em>
=> y(x, t) = (0.03m) × cos[2π((0.20)/(2.4 m) + 0.50/(0.20 s))]
<em>Carefully solve the equation</em>
=> y(x, t) = (0.03m) × cos[2π((0.20)/(2.4 m)) + 2π(0.50/(0.20 s))]
=> y(x, t) = (0.03m) × cos[0.08π + 5π]
=> y(x, t) = (0.03m) × cos[5.08π]
=> y(x, t) = (0.03m) × cos[15.96]
=> y(x, t) = (0.03m) × cos[15.96]
=> y(x, t) = (0.03m) × -0.9684
=> y(x, t) = 0.029m
Therefore the displacement at those points is -0.029m
Also, the sign of the displacement shows that the direction of the wave is in the negative x direction.
Answer:
Explanation:
In order to answer this problem you have to know the depth of the column, we say R, this information is important because allows you to compute some harmonic of the tube. With this information you can compute the depth of the colum of air, by taking tino account that the new depth is R-L.
To find the fundamental mode you use:
n: mode of the sound
vs: sound speed
L: length of the column of air in the tube.
A) The fundamental mode id obtained for n=1:
B) For the 3rd harmonic you have:
C) For the 2nd harmonic:
Solid moves slightly in a fixed position
