With a tuning fork of 384 hz, resonance tube lengths are acheived at 0.647m and 1.09 m. What is the speed of sound?
frequency*wavelength=vP
Get your tube formulas. YOu know for some n, and n+1, the resonanance is at L those distances. Solve for wavellength.
To find the speed of sound using the given information, we can use the formula:
frequency * wavelength = speed of sound (v)
Since we know the frequency of the tuning fork (384 Hz), and we have resonance tube lengths at 0.647 m and 1.09 m, we can find the corresponding wavelengths.
The fundamental frequency (n=1) corresponds to the resonance tube length of 0.647 m, so let's find the wavelength for this resonance length. We'll call it λ₁.
λ₁ = 2 * 0.647 m = 1.294 m
The next harmonic frequency (n=2) corresponds to the resonance tube length of 1.09 m. We'll find the wavelength for this resonance length and call it λ₂.
λ₂ = 2 * 1.09 m = 2.18 m
Now we have the wavelengths for the fundamental frequency (λ₁) and the second harmonic (λ₂), and we know the frequency (384 Hz). Let's use the formula mentioned earlier:
frequency * wavelength = speed of sound (v)
For the fundamental frequency:
384 Hz * 1.294 m = v
For the second harmonic:
384 Hz * 2.18 m = v
By solving for v in both equations, we can find the speed of sound.
For the fundamental frequency:
v = 384 Hz * 1.294 m = 496.896 m/s
For the second harmonic:
v = 384 Hz * 2.18 m = 835.2 m/s
The speed of sound can be considered an average of these values, so we can take the average:
(v₁ + v₂) / 2 = (496.896 m/s + 835.2 m/s) / 2 = 666.048 m/s
Therefore, the speed of sound is approximately 666.048 m/s.