If you slosh the water in a bathtub at the correct frequency, the water rises first at one end and then at the other. Suppose you can make a standing wave in a 145 cm long tub with a frequency of 0.31 Hz. What is the velocity of the water wave?
That depends upon how many nodes are in the standing wave. If there is one in the middle, than the wavelength is 290 cm. Multiply that by the frequency for the wave velocity.
To find the velocity of the water wave, we can use the formula:
velocity = frequency * wavelength
We are given the frequency (f) as 0.31 Hz. To find the wavelength (λ), we need to use the formula:
wavelength = 2 * length
where the length (L) of the tub is 145 cm.
Substituting the values into the formulas, we have:
wavelength = 2 * 145 cm = 290 cm
Now we can calculate the velocity:
velocity = 0.31 Hz * 290 cm = 89.9 cm/s
Therefore, the velocity of the water wave is 89.9 cm/s.
To find the velocity of the water wave, we can use the formula: Velocity = Frequency * Wavelength.
First, we need to find the wavelength. In the case of a standing wave, the wavelength is twice the length of the tub, so the wavelength is 2 * 145 cm = 290 cm.
Next, we use the formula: Velocity = Frequency * Wavelength.
We plug in the values:
Velocity = 0.31 Hz * 290 cm.
Next, we need to convert the wavelength from centimeters to meters since velocity is typically measured in meters per second. There are 100 centimeters in one meter, so we divide the wavelength by 100: 290 cm / 100 = 2.9 meters.
Finally, we multiply the frequency by the converted wavelength:
Velocity = 0.31 Hz * 2.9 meters = 0.899 meters per second.
Therefore, the velocity of the water wave in the tub is approximately 0.899 meters per second.