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Vedmedyk [2.9K]
4 years ago
15

E fundamental frequency of an open organ pipe corresponds to the middle c (261.6 hz on the chromatic musical scale). the third r

esonance of a closed organ pipe has the same frequency. (assume that the speed of sound in air is 343 m/s.) (a) what is the length of the open pipe
Physics
1 answer:
luda_lava [24]4 years ago
8 0

The wavelength of the third resonance of the closed organ pipe is equal to the ratio between the speed of sound and the frequency of the 3rd harmonic:

\lambda_3 = \frac{c}{f_3}=\frac{343 m/s}{261.6 Hz} =1.31 m

The relationship between length of a closed pipe and wavelength of the standing waves inside is:

L=\frac{n}{4}\lambda_n

where n is the number of the harmonic. In this case, n=3, so the length of the pipe is

L=\frac{3}{4}(1.31 m)=0.98 m

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4 years ago
A diffraction pattern is formed on a screen 130 cm away from a 0.420-mm-wide slit. Monochromatic 546.1-nm light is used. Calcula
notka56 [123]

Answer:

The fractional Intensity \frac{I}{I_{max}} = 0.0146

Given:

wavelength of the light, \lambda = 546.1 nm = 546.1\times 10^{-9} m

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Solution:

To calculate the fractional intensity, we use the given formula:

\frac{I}{I_{max}} = \frac{sin^{2}\delta }{\frac({\delta}{2})^{2}}             (1)

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For very small angle:                                        

\delta = \frac{\pi dy}{\lambda D}                                  (2)

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\delta = total phase angle

\theta = angle of deviation

Using eqn (2):

\delta = \frac{\pi \times 0.42\times 10^{-3}\times 4.1\times 10^{-3} }{546.1\times 10^{-9}\times 1.3} = 7.6202 radians

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