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3 years ago

A closed pipe and an open pipe have their first overtones identical in frequency. their lengths are in the ratio?

1 answer:

5 0

You should mention that sound waves are generated in identical conditions i.e the speed of sound is same in the two experiments.
In that case the ratio is
2v/2L1 : 3v/4L2 = 4L2 : 3L1 .

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4 years ago

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3 years ago

Calculate the first and second order angles for light of wavelength 400. nm and 700. nm of the grating contains 1.00 x 104 lines

Verdich [7]

Answer:

$23.58^{\circ}$ and $53.13^{\circ}$

$44.43^{\circ}$ , second order does not exist

Explanation:

n = Number of lines grating = $1\times10^4\ \text{Lines/cm}$

$\lambda$ = Wavelength

m = Order

Distance between slits is given by

$d=\dfrac{1}{n}\\\Rightarrow d=\dfrac{1}{1\times 10^4}\\\Rightarrow d=10^{-6}\ \text{m}$

$\lambda=400\ \text{nm}$

m = 1

We have the relation

$d\sin\theta=m\lambda\\\Rightarrow \theta=\sin^{-1}\dfrac{m\lambda}{d}\\\Rightarrow \theta=\sin^{-1}\dfrac{1\times 400\times 10^{-9}}{10^{-6}}\\\Rightarrow \theta=23.58^{\circ}$

m = 2

$\theta=\sin^{-1}\dfrac{2\times 400\times 10^{-9}}{10^{-6}}\\\Rightarrow \theta=53.13^{\circ}$

The first and second order angles for light of wavelength 400 nm are $23.58^{\circ}$ and $53.13^{\circ}$ .

$\lambda=700\ \text{nm}$

m = 1

$\theta=\sin^{-1}\dfrac{1\times 700\times 10^{-9}}{10^{-6}}\\\Rightarrow \theta=44.43^{\circ}$

m = 2

$\theta=\sin^{-1}\dfrac{2\times 700\times 10^{-9}}{10^{-6}}$

Here $\dfrac{2\times 700\times 10^{-9}}{10^{-6}}=1.4>1$ so there is no second order angle for this case.

The first order angle for light of wavelength 700 nm are $44.43^{\circ}$ .

Second order angle does not exist.

5 0

3 years ago