Question

Two boats are anchored in the harbor, separated by a horizontal distance of 12 m. The boats bob up and down as waves enter the harbor. When one boat is at its highest point, the other is at its lowest point and there are no wave crests between them. Each boat makes exactly 2 complete up-and-down cycles every 10.0 s. The vertical distance between a boat's highest and lowest position is 2.4 m. Determine the wavelength, frequency, period, amplitude and speed of the waves. Include at least two significant digits on your answer. Wavelength (m): Frequency (Hz): Period (s): Amplitude (m): Speed (m/s):

Answer 1

Answer: Here's my answer, sorry if it detailed.

Step-by-step explanation:

To determine the properties of the waves, let's analyze the given information step by step:

1. Wavelength (λ): The wavelength is the distance between two consecutive wave crests (or troughs). In this case, the distance between the boats is equal to the wavelength since there are no wave crests between them. Therefore, the wavelength is 12 m.

2. Frequency (f): Frequency is the number of complete cycles (or oscillations) per second. Since each boat makes exactly 2 complete up-and-down cycles every 10.0 s, the total number of cycles for both boats is 4. Thus, the frequency is 4 cycles / 10.0 s = 0.4 Hz.

3. Period (T): Period is the time taken for one complete cycle. It is the inverse of frequency. So, T = 1 / f = 1 / 0.4 Hz = 2.5 s.

4. Amplitude (A): The amplitude is the maximum displacement of a wave from its equilibrium position. In this case, the vertical distance between a boat's highest and lowest position is given as 2.4 m. Hence, the amplitude is 2.4 m.

5. Speed (v): The speed of a wave is the product of its frequency and wavelength. So, v = f * λ = 0.4 Hz * 12 m = 4.8 m/s.

To summarize:

Wavelength (λ): 12 m

Frequency (f): 0.4 Hz

Period (T): 2.5 s

Amplitude (A): 2.4 m

Speed (v): 4.8 m/s

These values describe the properties of the waves between the two boats in the harbor.