A water wave is generated in a ripple tank by an oscillator that vibrates 50 times in 30 seconds. A given trough of the wave travels 50.0 cm in 15 seconds. What is the wavelength of the water wave? Produce all your workings.

frequency*wavelength= velocity

50/30*wavelength=.5/15

solve for wavelength.

To determine the wavelength of the water wave, we need to use the formula:

wavelength (λ) = velocity (v) / frequency (f)

However, we're not given the velocity, but we are given some information about the trough of the wave. We know that the given trough travels 50.0 cm in 15 seconds. From this information, we can calculate the velocity using the formula:

velocity = distance / time

Let's calculate the velocity first:

velocity = 50.0 cm / 15 s

To perform the calculation, we need to ensure that the units are consistent. Let's convert cm to meters:

velocity = (50.0 cm / 100) m / 15 s
velocity = 0.5 m / 15 s
velocity = 0.0333 m/s (rounded to four decimal places)

Now that we have the velocity, we can calculate the wavelength:

wavelength = velocity / frequency

However, we weren't directly given the frequency, but we know that the oscillator vibrates 50 times in 30 seconds.

frequency = number of oscillations / time

frequency = 50 / 30

Let's calculate the frequency:

frequency = 50 / 30
frequency = 1.6667 Hz (rounded to four decimal places)

Now, we can calculate the wavelength:

wavelength = velocity / frequency
wavelength = 0.0333 m/s / 1.6667 Hz
wavelength ≈ 0.01998 m or 1.998 cm (rounded to four decimal places)

Therefore, the wavelength of the water wave is approximately 0.01998 meters or 1.998 centimeters.