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 find the frequency of the tuning fork, we need to use the equation for the speed of sound:
speed of sound = frequency * wavelength
In this case, the wavelength is the distance between consecutive resonance points, which is the distance the water level is lowered each time we hear resonance. Let's call this distance "d".
Given that resonance is observed when the water level drops by 18 cm and again when it drops by 54 cm, the wavelength is the difference between these two distances, which is:
wavelength = 54 cm - 18 cm = 36 cm
Now, we need to convert the wavelength from centimeters to meters because the speed of sound is typically given in meters per second. Since 1 meter is equal to 100 centimeters, the wavelength in meters is:
wavelength = 36 cm * (1 m / 100 cm) = 0.36 m
Next, we need to determine the speed of sound. The speed of sound depends on various factors, including temperature, humidity, and the medium through which it travels. For example, in dry air at room temperature, the speed of sound is approximately 343 meters per second.
Finally, we can rearrange the equation to solve for the frequency:
frequency = speed of sound / wavelength
Using the speed of sound as 343 m/s and the wavelength as 0.36 m, we can substitute these values into the equation to calculate the frequency:
frequency = 343 m/s / 0.36 m
Calculating this gives us:
frequency ≈ 952.78 Hz
Therefore, the frequency of the tuning fork is approximately 952.78 Hz.