To solve for the velocity of sound in air, we can use the formula:
v = fλ
where:
v = velocity of sound
f = frequency of the wave
λ = wavelength of the wave
In this problem, we are given the frequency and the length of the string, but we need to find the wavelength. For a string fixed at both ends, the wavelength is given by:
λ = 2L/n
where:
L = length of the string
n = harmonic number
In this case, the string is fixed at both ends, so the harmonic number will be an odd number:
n = 1, 3, 5, ...
We are given that the maximum frequency is 800 Hz, which corresponds to the fundamental frequency (n = 1). Therefore:
λ = 2L/n = 2(1.25 m)/1 = 2.5 m
Now we can substitute the values into the formula for the velocity of sound:
v = fλ = (800 Hz)(2.5 m) = 2000 m/s
Therefore, the velocity of sound in air is 2000 m/s.