20 wave crests pass a fisherman in one minute if the wave crests are 2.0 m apart find:
Period
Frequency
Speed of waves
PLEASE HELP MEEEEEE
Distance between wave crests, λ
= wave length
= 2 metres
Time complete one wave
= period
= 60 s / 20 waves
= 3 s
Frequency f is number of waves per second
= (1/3) Hz
Speed = f * λ
= (1/3)Hz * 2m
=2/3 m/s
To find the period, frequency, and speed of waves, we first need to understand the basic definitions of each term:
1. Period (T): The period of a wave is the time it takes for one complete cycle to pass a given point. It is usually measured in seconds.
2. Frequency (f): The frequency of a wave is the number of complete cycles passing a given point per second. It is the reciprocal of the period and is measured in Hertz (Hz).
3. Speed of waves (v): The speed of a wave is the distance it travels in a given amount of time. It is usually measured in meters per second (m/s).
Now, let's calculate each value step by step:
Step 1: Find the period (T):
The period can be calculated using the formula:
T = 1 / f
where f is the frequency.
To calculate the frequency, we count the number of wave crests passing a given point per minute and convert it to the frequency per second. In this case, 20 wave crests pass in one minute.
Frequency (f) = Number of wave crests / Time
= 20 / 60 (since 1 minute = 60 seconds)
= 1/3 Hz (rounding to two decimal places)
Now, we can use the formula to find the period:
T = 1 / f
= 1 / (1/3)
= 3 seconds
Therefore, the period of the wave is 3 seconds.
Step 2: Find the frequency (f):
We have already calculated the value of frequency as 1/3 Hz.
So, the frequency of the wave is 1/3 Hz.
Step 3: Find the speed of waves (v):
The speed of waves can be calculated using the formula:
v = λ x f
where v is the speed, λ (lambda) is the wavelength, and f is the frequency.
In this case, the distance between the wave crests, known as the wavelength (λ), is given as 2.0 meters.
v = 2.0 x (1/3)
= 0.67 m/s (rounded to two decimal places)
Therefore, the speed of the waves is 0.67 m/s.
To summarize:
- The period of the wave is 3 seconds.
- The frequency of the wave is 1/3 Hz.
- The speed of the waves is 0.67 m/s.