2. Travelling Harmonic Waves
• The displacement of any element of a medium
from its equilibrium position changes with time
as a wave passes through it (Hawkes, 2015).
3. Equation
Can exist as two forms:
• When the wave is travelling in the direction of
decreasing x
• When the wave is travelling in the direction of
increasing x
4. Equation
• Wavelength can be solved by:
Where λ = wavelength
• Time period can be solved by:
Where T = period
5. Equation
• With all relationships plugged into the initial
harmonic wave equation, we get:
6. Application
• A 90kg body builder is
looking to slim down to a
sizeable 85kg. To do this
he must exercise with
cardio. A good exercise
that is good cardio work
and features aspects of
travelling harmonic waves
is the battle rope. Each
time the arm moves, it
generates a pulse thus
creating a wave.
• Note: To simplify things, we will only
be examining the wave of one rope.
Image from: http://www.garage-
gyms.com/battle-rope-workouts/
7. Question
• The following values were determined:
A = 0.50 m λ = 0.75 m T = 0.25 s
1. What kind of wave is this? Explain.
2. Determine the harmonic wave equation in the
form of D(x,t).
3. Calculate the speed of the rope.
8. Solution to Q1
• This is a transverse wave since the constituents
of the medium moves perpendicular to the
direction of propagation of the wave.
9. Solution to Q2
• Because we are given the the wavelength (λ) and
period (T), we must use to it solve for k and ω
respectively.
Solving for k Solving for ω
10. Solution to Q2 cont.
• Using the new values we can find the equation
of the wave function.
A = 0.50 m k = 8.38 rad/m ω = 25.13 rad/s
• Recall that the original formula is:
• Plugging in values gives us the equation:
11. Solution to Q3
• To calculate the speed, we use the equation:
• Using values from the previous question, we can
solve for speed:
