A bird sits on a pole and watches waves. The wave crests are 1.0 meter apart. If one wave crest passes the pole each second, what is the speed of the wave? .
What is the period of the wave? .
What is the frequency of the wave? .
If the waves change so that the distance between crests was 1.5 meters, and one wave crest passes the pole each second, what is the speed of the wave? .
What is the new period of the wave? .
What is the new frequency of the wave? .
The formula for frequency is: frequency = 1 / T, where T = Period. That is e.g. "cycles per second".
The formula for time is: T (Period) = 1 / frequency.
Note: T = Period and t = Time
You have six waves passing and the distance between each wave is 12m. So, 5 x 12= 60m.
Therefore, the speed is 60 m/s
To find the answers, we can use the following formulas:
Speed of a wave (v) = Wavelength (λ) x Frequency (f)
Period (T) = 1 / Frequency (f)
Let's calculate the answers step-by-step for the given information:
1. The wave crests are 1.0 meter apart, and one wave crest passes the pole each second.
a) Speed of the wave (v):
v = 1.0 meter (wavelength) x 1 wave/second (frequency)
v = 1.0 meter/second
b) Period (T):
T = 1 / 1 wave/second (frequency)
T = 1 second
c) Frequency (f):
f = 1 wave/second
2. If the distance between crests is changed to 1.5 meters, and one wave crest still passes the pole each second.
a) Speed of the wave (v):
v = 1.5 meters (wavelength) x 1 wave/second (frequency)
v = 1.5 meters/second
b) New Period (T):
T = 1 / 1 wave/second (frequency)
T = 1 second
c) New Frequency (f):
f = 1 wave/second
To summarize the answers:
For the original wave:
- Speed of the wave = 1.0 meter/second
- Period = 1 second
- Frequency = 1 wave/second
For the new wave with a larger distance between crests:
- Speed of the wave = 1.5 meters/second
- Period = 1 second
- Frequency = 1 wave/second
To find the speed of the wave, you can use the formula:
Speed (v) = Wavelength (λ) × Frequency (f)
In this case, you are given the wavelength (the distance between wave crests) as 1.0 meter and the frequency (the number of wave crests passing the pole per second) as 1.0 second. So, the speed of the wave is:
Speed = 1.0 meter × 1.0 wave crest/second = 1.0 meter/second
The period of a wave is the time it takes for one complete wave cycle to pass a given point. It is the reciprocal of the frequency, so in this case, the period is:
Period = 1/frequency = 1/1.0 = 1.0 second
The frequency of the wave is the number of wave crests passing a given point per second. In this case, the frequency is already given as 1.0 wave crest/second.
Now, let's consider the new scenario where the distance between wave crests is 1.5 meters, but the frequency remains the same (1.0 wave crest/second).
Using the same formula as before:
Speed = Wavelength × Frequency
Given the new wavelength (Δλ) as 1.5 meters and frequency (f) as 1.0 wave crest/second, the speed of the wave is:
Speed = 1.5 meters × 1.0 wave crest/second = 1.5 meters/second
The new period can be calculated as the reciprocal of the frequency, so:
New Period = 1/frequency = 1/1.0 = 1.0 second
Since the frequency remains the same at 1.0 wave crest/second, the new frequency is also 1.0 wave crest/second.
To summarize:
- Original speed of the wave: 1.0 meter/second
- Original period of the wave: 1.0 second
- Original frequency of the wave: 1.0 wave crest/second
- New speed of the wave: 1.5 meters/second
- New period of the wave: 1.0 second
- New frequency of the wave: 1.0 wave crest/second