In a resonant experiment, the successive positions of resonance occur when the distance between the source and the reflecting surface is equal to an integral multiple of half the wavelength of the sound wave.
The formula relating wavelength (λ), velocity (v), and frequency (f) is:
v = λ * f
where v is the velocity of sound in air.
In the given problem, the first successive position of resonance occurs at a length of 15.4 m, which corresponds to half a wavelength, and the second successive position occurs at a length of 48.6 m, which corresponds to one and a half wavelengths.
We can set up the following equations based on the given information:
15.4 m = (1/2) * λ 48.6 m = (3/2) * λ
To solve for the wavelength, we can subtract the first equation from the second:
48.6 m - 15.4 m = (3/2) * λ - (1/2) * λ
33.2 m = λ
Now, we can use the velocity of sound to find the frequency:
v = λ * f
3400 m/s = 33.2 m * f
Dividing both sides by 33.2 m:
f = 3400 m/s / 33.2 m ≈ 102.41 Hz
Therefore, the frequency of the source in this resonant experiment is approximately 102.41 Hz.