-- Equations #2 and #6 are both the same equation,
and are both correct.
-- If you divide each side by 'wavelength', you get Equation #4,
which is also correct.
-- If you divide each side by 'frequency', you get Equation #3,
which is also correct.
With some work, you can rearrange this one and use it to calculate
frequency.
Summary:
-- Equations #2, #3, #4, and #6 are all correct statements,
and can be used to find frequency.
-- Equations #1 and #5 are incorrect statements.
Answer:
0.21%
Explanation:
We are given;
Mass; m = 100 kg
Diameter; d = 2.2 mm = 2.2 × 10^(-3) m
Young's modulus; E = 12.5 x 10^(10) N/m².
Formula for area is;
A = πd²/4
A = (π/4) x (2.2 x 10^(-3))²
A = 3.8 x 10^(-6) m²
Force; F = mg
g is acceleration due to gravity and has a constant value of 9.8 m/s²
F = 100 × 9.8
F = 980 N
Formula for young's modulus is;
E = Stress/strain
Formula for stress = F/A
Formula for strain = ΔL/L
Thus;
E = (F/A)/(ΔL/L)
Making ΔL/L the subject, we have;
ΔL/L = (F/A)/E
Plugging in the relevant values;
ΔL/L = 980/(3.8 x 10^(-6) × 12.5 × 10^(10))
ΔL/L = 0.0021
Then percentage increase in length of a wire = 0.0021 × 100% = 0.21%
Answer:
y(x, t) = A Sin(ωt ± kx)
Explanation:
Waves can be classifies as either stationary (standing), or progressive (travelling). A progressive wave is one the is a traveling wave, transferring energy along its path. While a stationary wave seems not to be moving.
The general equation for a progressive wave is;
y(x, t) = A Sin(ωt ± kx)
Where: A is its amplitude, t is the time, k is the wave number.
When the wave travels in the positive x-axis direction, the equation changes to;
y(x, t) = A Sin(ωt - kx)
When it travels in the negative x- axis direction, the equation becomes;
y(x, t) = A Sin(ωt + kx)
NB: ω = 2
f and k = 2
/λ.