When you slosh the water back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65 cm -wide tub is 0.75 Hz .
What is the speed of the water wave?
To find the speed of the water wave, we can use the formula:
Speed = Frequency x Wavelength
Given that the frequency is 0.75 Hz and the width of the tub is 65 cm, we need to find the wavelength.
The wavelength of a standing wave in a 65 cm-wide tub can be found using the formula:
Wavelength = 2 x Tub Width
Plugging in the values, we get:
Wavelength = 2 x 65 cm = 130 cm
Now we can calculate the speed:
Speed = Frequency x Wavelength
= 0.75 Hz x 130 cm
= 97.5 cm/s
Therefore, the speed of the water wave is 97.5 cm/s.