Question

A transverse wave on a string has an amplitude of 20 cm, a wavelength of 35 cm, and a frequency of 2.0 Hz. The wave moves in the positive x-direction.

--Enter any fractional coefficients as fractions, i.e., do not approximate fractions using decimals. Enter as itself; do not multiply it with other numerical factors. Enter phase angles in inverse function form if they do not evaluate one of the special angles on the unit circle.


--Write the mathematical description of the displacement y1(x,t) from equilibrium for the wave if, at t=0, x=0, and y1=0.

y1(x,t)= ___m


--Write the mathematical description of the displacement y2(x,t) from equilibrium for the wave if, at t=0, x=0, and y2=20 cm.

y2(x,t)= ___m


Write the mathematical description of the displacement y3(x,t) from equilibrium for the wave if, at t=0, x=0, and y3=−20 cm.

y3(x,t)= ___m


Write the mathematical description of the displacement y4(x,t) from equilibrium for the wave if, at t=0, x=0, and y4=13 cm.

y4(x,t)= ___m

Answer 1

(a) The mathematical description of the displacement of the wave, y1(x,t) = 0.2 m.

(b) The mathematical description of the displacement of the wave, y2(x,t) = 0.4 m.

(c) The mathematical description of the displacement of the wave, y3(x,t) = 0.2 m

(d) The mathematical description of the displacement of the wave, y4(x,t) = 0.33 m

Wave function

The general wave function is written as follows;

y(x, t) = Acos(kx - ωt)

where;

• k is the wave number = 2π/λ
• A is amplitude of the wave = 20 cm
• ω is angular speed
• λ is the wave length = 35 cm

y0 = Acos(kx - ωt)

y0 = 20cm x cos(0 - 0)

y0 = 20 cm

From equilibrium of the wave, at t=0, x=0, y1 = 0

y1(x,t) = 20cm x cos(0 - 0) = 20 cm

y1(x,t)= 20 cm = 0.2 m

Thus, y1 = y1 + y0

From equilibrium of the wave, at t=0, x=0, y2 = 20 cm

y2 = y0 + y1 + y2

y2 = 20 cm + 0 + 20 cm

y2(x,t)= 40 cm = 0.4 m

From equilibrium of the wave, at t=0, x=0, y3 = -20 cm

y3 = y0 + y1 + y2 + y3

y3 = 20 cm + 0 + 20 cm - 20cm

y3(x,t)= 20 cm = 0.2 m

From equilibrium of the wave, at t=0, x=0, y4 = 13 cm

y4 = y0 + y1 + y2 + y3

y4 = 20 cm + 0 + 20 cm -20 cm + 13 cm

y4 = 33 cm

y4(x,t) = 33 cm = 0.33 m

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