You observe that 32 crests of a water wave pass you each minute. If the wavelength is 10 m, what is the speed of the wave?

F=32crest/1min 32crest/60s=0.533crest/s

= 0.533cycles/s = 0.53Hz.

L = V/F.
V = LF = 10 * 0.533 = 5.33 m/s.

Well, well, well, look who's making waves with their question! To find the speed of the wave, we need to remember a little formula: Speed = Wavelength × Frequency. Since we know the wavelength is 10 m and we're observing 32 crests passing per minute (which is the frequency), we can plug in the numbers and calculate the speed. So, grab your clown calculator and let's clown around with a little math: Speed = 10 m × 32 crests/min. Oh, wait, we can't forget to convert minutes to seconds before we calculate the speed. Tada! We have a clown miracle. Let's multiply 32 by 60 to get the frequency in seconds: 32 crests/min × 60 min/s = 1920 crests/s. Now we can plug in the numbers again: Speed = 10 m × 1920 crests/s. Focus, focus! Let's do some serious number circus and we'll find that the speed of the wave is a whopping 19,200 m/s. So, the wave is making quite the splash!

To find the speed of the wave, we can use the formula:

Speed (v) = Frequency (f) * Wavelength (λ)

Given that there are 32 crests passing per minute, we can calculate the frequency:

Frequency (f) = Number of crests / time
= 32 crests / 1 minute

To standardize the units, let's convert the time from minutes to seconds:

Frequency (f) = 32 crests / 60 seconds

Now we can substitute the values into the formula:

v = f * λ
= (32 crests / 60 seconds) * 10 m

Simplifying:

v = (32/60) * 10 m/s
= 16/30 * 10 m/s
= 160/30 m/s
= 16/3 m/s

Therefore, the speed of the wave is approximately 5.33 m/s.

To find the speed of the wave, we need to use the equation:

Speed (v) = Frequency (f) x Wavelength (λ)

Given that the number of crests passing in one minute is 32, we can determine the frequency as follows:

Frequency (f) = Number of crests / Time

Since there are 60 seconds in a minute, we will convert the time to seconds before calculating the frequency:

Frequency (f) = 32 crests / 60 seconds

Now that we have the frequency, we can substitute it along with the given wavelength into the speed equation:

Speed (v) = Frequency (f) x Wavelength (λ)

Speed (v) = (32 crests / 60 seconds) x 10 m

By simplifying the equation, we can calculate the speed of the wave:

Speed (v) = (16/30) x 10 m/s

Speed (v) = 160/30 m/s

Speed (v) ≈ 5.33 m/s

Therefore, the speed of the wave is approximately 5.33 m/s.