A rock dropped into a pond produces a wave
that takes 14.6 s to reach the opposite shore,21.1 m away. The distance between consecutive crests of the wave is 5.3 m.
What is the frequency of the wave?
Well, first of all, I just have to say, that's one patient wave! Taking its sweet time to reach the other shore in 14.6 seconds. Must have stopped for a coffee break along the way!
Now, let's get down to business. To find the frequency of the wave, we need to figure out how many crests pass a given point in a certain amount of time.
So, we know that the distance between consecutive crests is 5.3 meters. Now, if the wave travels a distance of 21.1 meters in 14.6 seconds, that means it passes through 4 crests (21.1 ÷ 5.3) in that time.
Therefore, the frequency of the wave is 4 crests / 14.6 seconds. And if my math skills haven't gone down the drain, that results in a frequency of approximately 0.274 crests per second.
So, in conclusion, the frequency of the wave is about 0.274 crests per second. It's quite the laid-back wave. Definitely not in any hurry!
To find the frequency of the wave, we first need to determine the period of the wave.
The period of a wave is the time it takes for one complete cycle of the wave to pass a given point. In this case, the complete cycle of the wave is the distance between two consecutive crests, which is given as 5.3 m.
Since the wave takes 14.6 s to reach the opposite shore, we can calculate the period of the wave using the formula:
Period (T) = Total time (t) / Number of cycles (n)
Number of cycles (n) = Total distance (d) / Distance per cycle (wavelength)
In this case, the total distance is 21.1 m, and the distance per cycle is 5.3 m.
Number of cycles (n) = 21.1 m / 5.3 m = 4 cycles
Now we can calculate the period of the wave:
Period (T) = 14.6 s / 4 cycles = 3.65 s
Finally, we can calculate the frequency of the wave using the formula:
Frequency (f) = 1 / Period (T)
Frequency (f) = 1 / 3.65 s ≈ 0.27 Hz
Therefore, the frequency of the wave is approximately 0.27 Hz.