Physics Question please HELP

Question

A student carefully makes the following observations listening for the resonance points from a tuning fork vibrating above an adjustable length closed air column: Temperature is 13.3 °C. 1st Resonant Length(s): 8.3 cm Then they rush their following measurements for additional resonance points to finish the lab: L = 25 2 cm,L =58cm. 

 

a) Perform the necessary calculations to find the frequency of the unknown tuning fork.

 

b) Analyze all the data to see if they made any errors in their collection of observations.

Answer 1

For closed air columns, harmonics or resonance points occur at every odd harmonic#: 1st, 3rd, 5th, 7th, odd#th.
The length of the resonant wave, represented by L, in the closed air column for each harmonic is: L = 1/4λ, 3/4λ, 5/4λ, 7/4λ respectively.
Thus the wavelength, λ, for each harmonic is: (1st) λ = (4/1)L, (3rd) λ = (4/3)L, (5th) λ = (4/5)L, (7th) λ = (4/7)L.
We can use the relationship among the speed of sound, the wavelength and the frequency of the wave to make calculations: v = f • λ

GIVEN:
T = 13.3 °C
1st L = 8.3 cm = 0.083 m
2nd L = 25.2 cm = 0.252 m
3rd L = 58cm = 0.58 m

UNKNOWN:
f1 = ?
f2 = ?
f3 = ?
v of sound = ?

SOLUTION:
Speed of sound changes with air temperature. The speed of sound is 343.4 m/s at 20 C. The formula to calculate the speed is:v of sound = (343.4 m/s)± (0.6 m/s/C • ΔT), ΔT = |20 - air temp|, add if temperature > 20, subtract if < 20
v of sound = 343.4 - (6.7 x 0.6) = 339.38 m/s
λ1 = 4(L1) = 4(0.083 m) = 0.332 m
λ2 = 4/3(L2) = 4/3(0.252m) = 0.336 m
λ3 = 4/5(L3) = 4/5(0.58 m) = 0.464 m *appears to be a measuring error*
v = f •λ and so, f = v/λ
f1 = v/λ1 = (339.38 m/s / 0.332 m) = 1022.2 Hz
f2 = v/λ2 = (339.38 m/s / 0.336 m) = 1010.1 Hz
f3 = v/λ3 = (339.38 m/s / 0.464 m) = 731. 4 Hz

The third frequency calculation is "off" compared to the first two. Perhaps they used a different tuning fork or just made a careless/rushed measurement resulting in an error. I did not use sig figs for this problem.