A vertical tube with a tap at the base is filled with water, and a tuning fork vibrates over its mouth. As the water level is lowered in the tube, resonance is heard when the water level has dropped 18 cm, and again after 54 cm of distance exists from the water to the top of the tube. What is the frequency of the tuning fork?
To determine the frequency of the tuning fork, we can use the principle of resonance. Resonance occurs when the frequency of the tuning fork matches one of the natural frequencies of the air column in the tube.
Let's first calculate the wavelength of the sound wave that is producing resonance. The wavelength can be determined by taking the difference between the initial water level and the final water level, which is 54 cm - 18 cm = 36 cm.
Next, we need to find the corresponding frequency of the tuning fork. The speed of sound in air at room temperature is approximately 343 meters per second.
We can use the formula:
speed of sound = frequency x wavelength
Since the speed of sound is given in meters per second and the wavelength is in centimeters, we need to convert the wavelength to meters. There are 100 centimeters in 1 meter, so we divide the wavelength by 100 to convert it to meters.
36 cm / 100 = 0.36 meters
Now we can rearrange the formula to solve for the frequency:
frequency = speed of sound / wavelength
frequency ≈ 343 m/s / 0.36 m ≈ 952.78 Hz
Therefore, the frequency of the tuning fork is approximately 952.78 Hz.