A rock dropped into a pond produces a wave that takes 15.7 s to reach the opposite shore, 24.3 m away. The distance between consecutive crests of the wave is 3.5 m. What is the frequency of the wave?
Oh, waves and rocks! That's a rock-solid question. Let's dive into it and make a splash!
To find the frequency of the wave, we need to know the time it takes for one wave to pass a certain point. In this case, the time it takes for the wave to reach the opposite shore is given as 15.7 seconds.
Now, we know that the distance between consecutive crests of the wave is 3.5 meters. That means each crest travels a distance of 3.5 meters in 15.7 seconds.
To find the frequency, we need to divide the distance travelled by the crest (3.5 m) by the time it takes (15.7 s). So, the frequency would be:
Frequency = Distance / Time
Frequency = 3.5 m / 15.7 s
Calculating that, we get a frequency of approximately 0.22 Hz (rounded to two decimal places).
So, the frequency of the wave is rocking at around 0.22 Hertz!
To find the frequency of the wave, we need to use the formula:
Frequency (f) = Speed (v) / Wavelength (λ)
In this case, the speed of the wave can be determined by dividing the distance traveled by the time taken:
Speed (v) = Distance (d) / Time (t)
Given:
Distance = 24.3 m
Time = 15.7 s
By substituting the given values into the equation, we can find the speed of the wave:
Speed (v) = 24.3 m / 15.7 s
Speed (v) ≈ 1.547 m/s
Next, we need to determine the wavelength (λ) of the wave. The wavelength refers to the distance between two consecutive crests of the wave.
Given: Wavelength (λ) = 3.5 m
Now that we know the speed and wavelength, we can calculate the frequency:
Frequency (f) = Speed (v) / Wavelength (λ)
Frequency (f) = 1.547 m/s / 3.5 m
Frequency (f) ≈ 0.442 Hz
Therefore, the frequency of the wave is approximately 0.442 Hz.