A tuning fork is set into vibration above a vertical open tube filled with water. The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.175 m, and again at 0.345 m. What is the frequency (in hertz) of the tuning fork?
To determine the frequency of the tuning fork, we can use the formula for the speed of sound in air:
v = λ * f,
where v is the speed of sound, λ is the wavelength of the sound wave, and f is the frequency of the sound wave.
In this scenario, we know the distances at which the air in the tube resonates with the tuning fork, which corresponds to the half-wavelength of the sound wave in the tube. We can calculate the wavelength λ by using the difference between these two distances:
Δλ = 0.345 m - 0.175 m.
Since Δλ is the half-wavelength, we can double it to obtain the full wavelength:
λ = 2 * Δλ.
Next, we need to calculate the speed of sound in air. The speed of sound in air at room temperature is approximately 343 m/s. Therefore, we can substitute this value into the formula:
v = 343 m/s.
Now we can rearrange the equation to solve for the frequency:
f = v / λ = 343 m/s / (2 * Δλ).
Substituting the values we have:
f = 343 m/s / (2 * (0.345 m - 0.175 m)).
f = 343 m/s / (2 * 0.170 m).
Finally, we can evaluate the expression to find the frequency of the tuning fork:
f = 343 m/s / (2 * 0.170 m).
f = 343 m/s / 0.340 m.
f ≈ 1008.82 Hz.
Therefore, the frequency of the tuning fork is approximately 1008.82 Hz.
1/4 lambda=.175
freq= velocitysound/lambda