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Travelling Harmonic Wave
Physics 101
Learning Object
A Harmonic wave is traveling on a string with a speed of 0.25 m/s.
The displacement of a portion of the string at x = 0.015 m is
observed to vary with time in the following equation:
D(0.015, t) = (0.09 m) sin (1.5 – 2.5t)
1.What is the frequency of the wave?
2.What is the value of the wavelength?
3.What is the phase constant?
4.Write and equation for this wave D(x, t)
Solutions:
General Equation: D(x, t) = Asin[2π/λ (x) - wt + φ]
At x = 0.015m
D(0.015, t) = (0.09)sin[2π/λ (0.015) – wt + φ]
1. Since w = 2.5
f = w/2 π = 2.5 / 2 π = 0.40 Hz
2. Since we know the velocity and the frequency, we can find the wavelength (λ)
V = λ f
λ = v/f = 0.25/0.40 = 0.63m
3. To find the phase constant, we use
2π/λ (0.015) + φ = 1.5
φ = 1.5 - 2π/λ (0.015)
= 1.5 - 2π/0.63 (0.015) = 1.4 rad
4. So the equation for this harmonic wave is:
D(x, t) = 0.09sin[2π/0.63 (0.015) – 2.5t + 1.4]

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Travelling Harmonic Waves

  • 1. Travelling Harmonic Wave Physics 101 Learning Object
  • 2. A Harmonic wave is traveling on a string with a speed of 0.25 m/s. The displacement of a portion of the string at x = 0.015 m is observed to vary with time in the following equation: D(0.015, t) = (0.09 m) sin (1.5 – 2.5t) 1.What is the frequency of the wave? 2.What is the value of the wavelength? 3.What is the phase constant? 4.Write and equation for this wave D(x, t)
  • 3. Solutions: General Equation: D(x, t) = Asin[2π/λ (x) - wt + φ] At x = 0.015m D(0.015, t) = (0.09)sin[2π/λ (0.015) – wt + φ] 1. Since w = 2.5 f = w/2 π = 2.5 / 2 π = 0.40 Hz 2. Since we know the velocity and the frequency, we can find the wavelength (λ) V = λ f λ = v/f = 0.25/0.40 = 0.63m 3. To find the phase constant, we use 2π/λ (0.015) + φ = 1.5 φ = 1.5 - 2π/λ (0.015) = 1.5 - 2π/0.63 (0.015) = 1.4 rad 4. So the equation for this harmonic wave is: D(x, t) = 0.09sin[2π/0.63 (0.015) – 2.5t + 1.4]