A tuning fork is held above an air column filled with water. The water level can be raised and lowered to

Question

change the length of the column. The shortest length of air column that produces a resonance is 0.30 m, and
the next resonance is heard when the air column is 0.80 m long.
a. Calculate the speed of sound at 25°C. [A2]
b. Calculate the wavelength of the sound wave produced by the tuning fork, along with the frequency of
the tuning fork. [A4]
c. If the water level is lowered again until a third resonance is heard, what is the length of the column at
that point? [A2]

Answer 1

To solve this problem, we can use the formula for the speed of sound in air, which is given by:

v = λf

Where:
v = speed of sound in air
λ = wavelength of the sound wave
f = frequency of the sound wave

a. To calculate the speed of sound at 25°C, we need to use the known wavelength and frequency of the sound wave. The wavelength can be found by subtracting the length of the air column for the second resonance from the length for the first resonance:

λ = 0.80 m - 0.30 m = 0.50 m

The frequency of the tuning fork can be found by using the formula:

f = v/λ

We need to calculate the speed of sound first, so we rearrange the formula:

v = λf

Substituting the known values gives:

v = (0.50 m)(f)

Now, we need to determine the frequency of the tuning fork. Since we don't have that information given in the problem, we can't solve this part of the problem.

b. To find the wavelength of the sound wave produced by the tuning fork, we know that the shortest length of the air column that produces resonance is 0.30 m. This length is half of a wavelength, so we can determine the wavelength:

λ = 2(0.30 m) = 0.60 m

Since we still don't have the frequency of the tuning fork, we can't solve this part of the problem.

c. If the water level is lowered again until a third resonance is heard, we need to determine the length of the air column at that point. Since the first resonance occurred at 0.30 m and the second resonance occurred at 0.80 m, the distance between these two resonances is equal to one wavelength. Therefore, the length of the air column for the third resonance would be:

Length for third resonance = 0.80 m + (0.80 m - 0.30 m) = 1.30 m