Interpreting the Wording of a Wave Problem: Understanding Speed and Period

In summary, the conversation discusses a problem in a physics class regarding the speed and period of a wave. The given wording of the problem leads to confusion as to whether the frequency should be 1 Hz or 2 Hz. While the answer key provides a solution of 1 Hz, it is argued that a frequency of 2 Hz is more accurate based on the wording.
  • #1
DarthVader
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Hello. A problem I have given my physics class states, "The distance between two crests in a wave is 1.5 m, and two crests pass a pole each second. What is the speed and period of the wave?" I believe the proper solution should be v = 3 m/s, and T = 0.5 s. In order for two crests to pass a given point each second (regardless of initial conditions), it seems that the frequency has to be 2 Hz. However, the solution manual has an answer of v = 1.5 m/s, and T = 1 s (so a frequency of 1 Hz). Could both answers be considered correct due to the wording of the problem?
 
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  • #2
DarthVader said:
Hello. A problem I have given my physics class states, "The distance between two crests in a wave is 1.5 m, and two crests pass a pole each second. What is the speed and period of the wave?" I believe the proper solution should be v = 3 m/s, and T = 0.5 s. In order for two crests to pass a given point each second (regardless of initial conditions), it seems that the frequency has to be 2 Hz. However, the solution manual has an answer of v = 1.5 m/s, and T = 1 s (so a frequency of 1 Hz). Could both answers be considered correct due to the wording of the problem?
The wording is a bit wonky, but because of the solution, the wording can be interpreted as: One wavelength of a wave goes by a point every second (because one wavelength is the distance between two crests). Thus, the period is one second and the speed can be determined by dividing the wavelength by the period.
 
  • #3
Tom MS said:
The wording is a bit wonky, but because of the solution, the wording can be interpreted as: One wavelength of a wave goes by a point every second (because one wavelength is the distance between two crests). Thus, the period is one second and the speed can be determined by dividing the wavelength by the period.
I would say that the wording is wrong rather than just wonky.

It says two crests in each second. That says that if I choose to start counting a second at the bottom of a trough that there will still be two crests before that second ends. That is compatible with two periods per second. It is not compatible with one period per second.
 

1. What is the relationship between speed and period of a wave?

The speed of a wave is directly proportional to its period. This means that as the speed of a wave increases, its period also increases. Conversely, as the speed decreases, the period also decreases. This relationship is known as the wave speed equation: speed = wavelength/period.

2. How does the wavelength affect the speed and period of a wave?

The wavelength of a wave has an inverse relationship with its speed and period. This means that as the wavelength increases, the speed and period of the wave decrease. Similarly, as the wavelength decreases, the speed and period increase. This is because the longer the wavelength, the greater the distance the wave needs to travel in a given period of time, resulting in a slower speed and longer period.

3. Can the speed and period of a wave be changed?

Yes, the speed and period of a wave can be changed by altering the properties of the medium through which the wave is traveling. For example, the speed of a sound wave can be changed by changing the temperature or pressure of the medium it is traveling through. The period of a wave can also be changed by altering the frequency, which is the number of complete wave cycles that occur in a given time period.

4. How are the speed and period of a wave related to its amplitude?

The amplitude of a wave, which is the maximum displacement of the wave from its equilibrium position, does not have a direct relationship with the speed and period of the wave. The speed and period are determined by the properties of the medium, while the amplitude is determined by the energy of the wave. However, a higher amplitude wave may appear to have a shorter period due to the increased energy and frequency of the wave.

5. What is the difference between the speed and period of a wave?

The speed of a wave refers to how fast the wave is traveling through the medium, while the period refers to the time it takes for one complete wave cycle to occur. In other words, the speed of a wave tells us how far the wave travels in a given amount of time, while the period tells us how long it takes for the wave to complete one full cycle. These two properties are related but represent different aspects of a wave's behavior.

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