Physics 101 LOProperties 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) Amplitudeb) Wavelength, λc) 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, fe) Wave Speed, v

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 = λ f .