Alex is practicing ribbon dancing and creates a continuous wave that travels along her ribbon in simple harmonic motion. The graph shows one cycle of the ribbon wave passing through point Z. The summary finds: (1) The amplitude is 0.5m, the maximum displacement from the horizontal axis. (2) The wavelength is 2.5m, the distance between consecutive crests/troughs. (3) The wave number is 4π/5 rad/m, representing the distance traveled within one wavelength. (4) The period is 4s and frequency is 1/4 Hz, the time and rate of one full wave passing point Z. (5) The wave speed is 5/

1. Physics 101 LO
Properties of Harmonic Waves
Alex, a ribbon dancer, is practicing her routine for an upcoming competition. Often, she
oscillates the ribbon and creates a continuous wave that travels along the string in simple
harmonic motion. A snapshot of her ribbon undergoing these conditions is shown above.
Find the following:
a) Amplitude
b) Wavelength, 𝜆
c) Wave Number, k
If one wave cycle produced by her ribbon goes through point Z it is represented by the
graph above. Find the following:
d) Period, T and Wave Frequency, f
e) Wave Speed, v

2. Solutions
a) Amplitude = 0.5 [m]
The amplitude is equal to the maximum displacement from the horizontal axis.
Basically, it is equal to the highest point starting from the x-axis. Amplitude is
always positive.
b) Wavelength = 2.5 [m]
The wavelength is the distance between two consecutive crests/trough. It is equal to
length that it takes for the wave to repeat itself.
c) Wave Number = 4pi/5 [rad/m]
The wave number shows the frequency or number of waves given over a certain
distance. It represents the distance travelled within one wavelength and is given by
k = 2pi/ 𝜆.
d) Period = 4s Wave frequency = ¼ Hz
The period is the time it takes to complete one cycle and the wave frequency is
equal to 1/T. In this situation the frequency represents the number of full waves
passing through point Z in 1second.
e) Wave Speed = 5/6 [m/s]
The wave speed corresponds to the speed at which a wave passes through a fixed
point. In this particular case, it would be point Z. Since we know the frequency of the
wave and the wavelength we are able to determine the wave speed. The wave speed
is given by v = 𝜆𝑓.