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

[DarthVader]

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?

 

[Tom MS]

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.

 

[jbriggs444]

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.