learning object 1
TRANSCRIPT
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: