A woman is sitting in a boat at anchor on a lake. Her boat bobs up and down once every 2.0·s. She notices that when the front of her 3.0·m long boat is at one wave crest, a second crest is at the middle of her boat, and a third is at the end.
What is the frequency of the waves? ____ Hz.
What is their wavelength? _____ m.
What is their speed? _____
Can someone explain how to get these?
You told me the period was 2 s so the frequency is (1/2) Hz
Two complete wavelengths along 3 meter boat
so Lambda = 3/2 = 1.5 meters
speed = distance/time = 1.5/2 = .75 m/s
To find the frequency of the waves, we need to determine the time it takes for the boat to complete one up-and-down motion. This is given in the question as 2.0 seconds. Therefore, the frequency can be calculated by taking the reciprocal of the time period:
Frequency = 1 / Time Period
Frequency = 1 / 2.0 s
Frequency = 0.5 Hz
So, the frequency of the waves is 0.5 Hz.
To find the wavelength of the waves, we need to analyze the position of the wave crests on the boat. The question states that when the front of the 3.0 m long boat is at one wave crest, a second crest is at the middle of her boat, and a third is at the end. This indicates that one complete wave cycle corresponds to the length of the boat.
Since we know the length of the boat is 3.0 m, the wavelength will also be equal to the length of the boat:
Wavelength = Length of the Boat
Wavelength = 3.0 m
So, the wavelength of the waves is 3.0 m.
To find the speed of the waves, we can use the equation:
Speed = Wavelength * Frequency
Using the values we have determined:
Speed = 3.0 m * 0.5 Hz
Speed = 1.5 m/s
So, the speed of the waves is 1.5 m/s.