To find the wavelength of a periodic wave, we first need to understand the relationship between wavelength, frequency, and speed of the wave. The wavelength is the distance between two consecutive points on the wave that are in phase, meaning they have the same amplitude and are at the same point in their cycle. The frequency is the number of complete waves that pass a given point in one second. The speed of the wave is the distance it travels in a certain amount of time.
In this case, we are given the distance between consecutive points on the wave, which is 420 cm. We are also told that there are 4 increments between the end of one full wave and the beginning of the other. This means that the distance between the end of one full wave and the beginning of the other is 4 times the distance between consecutive points, or 4*420 cm = 1680 cm.
To find the wavelength, we can use the formula: wavelength = speed/frequency. In this case, we do not have the speed or frequency, but we can use the relationship between them to find the wavelength. The speed of a wave is constant, so if we can find the frequency, we can then use it to find the wavelength.
To find the frequency, we can use the relationship: frequency = 1/period, where the period is the time it takes for one complete wave to pass a given point. In this case, we do not have the period, but we can calculate it by dividing the distance between the end of one full wave and the beginning of the other by the speed of the wave.
So, the period = distance/speed = 1680 cm/speed. Now, we can plug this into the formula for frequency: frequency = 1/period = 1/(1680 cm/speed) = speed/1680 cm.
Finally, we can plug this frequency into the formula for wavelength: wavelength = speed/frequency = speed/(speed/1680 cm) = 1680 cm.
Therefore, the wavelength of this wave is 1680 cm.
