A 1.0-m-tall vertical tube is filled with 20°C water. A tuning fork vibrating at 580 Hz is held just over the top of the tube as the water is slowly drained from the bottom. At what water heights, measured from the bottom of the tube, will there be a standing wave in the tube above the water? Express your answer numerically. If there is more than one answer, enter your answers in descending order separated by commas.

water heights of the tube are 0.851 m, 0.553 m, 0.255 m

Explanation:

given data

frequency = 580 Hz

temperature = 20°C

tube = 1 m

to find out

water heights of the tube

solution

we will apply here formula for length that is

length L = v (2n - 1) / 4f

here v is velocity o sound that is 343.2 m/s

so for n = 1

L = 343.2 (2 (1) - 1) / 4 (580) = 0.147931 m

for n = 2

L = 343.2 (2 (2) - 1) / 4 (580) = 0.443793 m

for n = 3

L = 343.2 (2 (3) - 1) / 4 (580) = 0.739655 m

for n = 4

L = 343.2 (2 (4) - 1) / 4 (580) = 1.035517 m is greater than 1

and so here height is measured less than 1 m

so water heights of the tube are 1 m - 0.147931 m, 1 m - 0.443793 m, 1 m - 0.739655 m

so water heights of the tube are 0.851 m, 0.553 m, 0.255 m