Essential Physics

Section 1 review

Waves are oscillations that travel. Waves have amplitude and frequency just like oscillators, but waves have the additional property of wavelength. A wave moves one wavelength forward in each cycle, so the speed of a wave is its wavelength divided by its period. This is equivalent to frequency times wavelength. A wave carries energy that is proportional to both amplitude and frequency. The higher the amplitude, the higher the energy at a given frequency. At equal amplitudes low-frequency waves have less energy than high-frequency waves. Transverse waves cause oscillations that are perpendicular to the direction of the wave’s motion, whereas longitudinal waves cause oscillations that are parallel to the wave’s motion. Read the text aloud

Read the text aloud

wave, wavelength, transverse, polarization, longitudinal

v = f λ

Review problems and questions

Height versus time and height versus distance for a transverse wave

The figure above shows a graph of the oscillation of a single point on a transverse wave as a function of time and a second graph of the waveform at a given instant as a function of distance. Use the graphs to answer the following questions.
1. What is the frequency of the wave?
2. What is the wavelength of the wave?
3. What is the amplitude of the wave?
4. What is the speed at which the wave propagates?

Answer:

0.5 Hz
20 cm
0.5 cm
0.1 m/s

Solution: The graph on the left shows the amplitude as a function of time and the graph on the right shows the amplitude in space.

The frequency can be seen from the height versus time graph. Note that one cycle takes 2 s. Therefore the frequency is $f = \frac{1}{T} = \frac{1}{2 s} = 0.5 Hz$
The graph on the right shows that the successive peaks of the wave are separated by 20 cm. The wavelength is therefore 20 cm.
Both graphs show that the wave goes up from the middle point by 0.5 cm and goes down from the middle point by −0.5 cm. The amplitude of the wave is therefore 0.5 cm.
Asked: the speed v of the wave depicted by the two graphs
There are several ways to solve this problem. Here are two methods:
1. Given: frequency f = 0.5 Hz (from part a), wavelength λ = 0.20 m (from Part b)
  Relationships: v = λf
  Solve: $v = λ f = 0.20 m \times 0.5 Hz = 0.1 m/s$ Answer: The speed of the wave is 0.1 m/s.
2. Given: From the left-hand graph, one cycle lasts for 2 s, so time t = 2 s. In the time of one period the wave travels one wavelength, so distance d = 0.20 m
  Relationships: v = d/t
  Solve: $v = \frac{d}{t} = \frac{0.20 m}{2 s} = 0.1 m/s$ Answer: The speed of the wave is 0.1 m/s.

A water wave has a frequency of 2 Hz and a wavelength of 1.5 m. What is the speed at which this wave travels?
1. 0.75 m/s
2. 1.5 m/s
3. 2.0 m/s
4. 3.0 m/s

The correct answer is d.

Solution:

v = λ f = (1.5 m) (2 Hz) = 3.0 m/s

1. If you are using a water tank in an investigation into waves, is a still image or a video a better choice for measuring wavelength?
2. How about for measuring frequency?
3. Amplitude?
4. Velocity of the wave?


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