Question

A wave has a wavelength of 3.0 m, a frequency of 25.0 Hz, and an amplitude of 14.0 cm. The wave travels in the positive x-direction and has a displacement of zero at t = 0 and x = 0. How many complete oscillations has the wave made at t = 20.0 s and x = 4.2 m?

Answer 1

A wave with a wavelength of 3.0 m and a frequency of 25.0 Hz has made 501.4 complete oscillations at t = 20.0 s and x = 4.2 m.

Step-by-step explanation:

A wave cycle consists of one complete wave starting at the zero point, going up to a wave crest, going back down to a wave trough, and back to the zero point again. The wavelength of a wave is the distance between any two corresponding points on adjacent waves. In this case, the wavelength of the wave is given as 3.0 m.

The frequency of a wave is the number of waves that pass a certain point in a specified amount of time. In this case, the frequency of the wave is given as 25.0 Hz.

The number of complete oscillations a wave has made can be calculated by multiplying the frequency of the wave by the time. At t = 20.0 s, the wave has made 25.0 Hz x 20.0 s = 500 complete oscillations. At x = 4.2 m, the wave has made 4.2 m / 3.0 m = 1.4 complete oscillations.

Therefore, at t = 20.0 s and x = 4.2 m, the wave has made 500 + 1.4 = 501.4 complete oscillations.

Answer 2

The total number of oscillations made by the wave during the time of travel is 1.4 Oscillations. Strictly speaking, the number of complete oscillations is 1.

Step-by-step explanation:

The required quantity is the number of complete oscillations made by the traveling wave. The amplitude time and frequency are not needed to calculate the number of oscillations as it is the ratio of the distance traveled to the wavelength( minimum distance that must be traveled to complete one oscillation) of the wave. So the total number of oscillations is 1.4 while the number of complete oscillations is 1 (strictly speaking). The detailed solution to this question can be found in the attachment below. Thank you!