Travelling Harmonic Waves

Alex Law36551142

PHYS 101 LF2

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).

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

Equation

• Wavelength can be solved by:

Where λ = wavelength

• Time period can be solved by:

Where T = period

Equation

• With all relationships plugged into the initial harmonic wave equation, we get:

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/

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.

Solution to Q1

• This is a transverse wave since the constituents of the medium moves perpendicular to the direction of propagation of the wave.

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

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:

Solution to Q3

• To calculate the speed, we use the equation:

• Using values from the previous question, we can solve for speed: