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tino4ka555 [31]
3 years ago
13

Two closed organ pipe gives 4 beats when sounded together at 5°C. Calculate the number of beats in 35°C​

Physics
1 answer:
Gre4nikov [31]3 years ago
7 0

Answer:

The number of beats is 10.58 in 35°C.

Explanation:

The beat frequency is given by : f₁-f₂

At 5°C, f₁-f₂ = 4

We need to find the number of beats in 35°C​.

The frequency in a standing wave is proportional to \sqrt T.

So,

\dfrac{f_1-f_2}{f_1'-f_2'}=\dfrac{\sqrt {T}}{\sqrt{T'}}\\\\f_1'-f_2'=(f_1-f_2)\times \dfrac{\sqrt{T'}}{\sqrt{T}}\\\\f_1'-f_2'=4\times \dfrac{\sqrt{35}}{\sqrt{5}}\\\\f_1'-f_2'=10.58

So, the number of beats is 10.58 in 35°C.

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A satellite in geostationary orbit is used to transmit data via electromagnetic radiation. The satellite is at a height of 35,000 km above the surface of the earth, and we assume it has an isotropic power output of 1 kW (although, in practice, satellite antennas transmit signals that are less powerful but more directional).

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How large does the radius R of the dish have to be to achieve an electric field vector amplitude of 0.1 mV/m at the receiver?

For simplicity, assume that your house is located directly beneath the satellite (i.e. the situation you calculated in the first part), that the dish reflects all of the incident signal onto the receiver, and that there are no losses associated with the reception process. The dish has a curvature, but the radius R refers to the projection of the dish into the plane perpendicular to the direction of the incoming signal.

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 The radius  of  the dish is R = 18cm

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  From the question we are told that

     The radius of the orbit is  = R = 35,000km = 35,000 *10^3 m

    The power output of the power is  P = 1 kW = 1000W

   The electric vector amplitude is given as E = 0.1 mV/m = 0.1 *10^{-3}V/m

    The area of thereciever  is   A_R = 5cm^2

Generally the intensity of the dish is mathematically represented as

         I = \frac{P}{A}

Where A is the area orbit which is a sphere so this is obtained as

          A = 4 \pi r^2

              = (4 * 3.142 * (35,000 *10^3)^2)

              =1.5395*10^{16} m^2

  Then substituting into the equation for intensity

          I_s  =  \frac{1000}{1.5395*10^{16}}

            = 6.5*10^ {-14}W/m2

 Now the intensity received by the dish can be mathematically evaluated as

              I_d = \frac{1}{2}  * c \epsilon_o E_D ^2

  Where c is thesped of light with a constant value  c = 3.0*10^8 m/s

              \epsilon_o is the permitivity of free space  with a value  8.85*10^{-12} N/m

              E_D is the electric filed on the dish

So  since we are to assume to loss then the intensity of the satellite is equal to the intensity incident on the receiver dish

      Now making the eletric field intensity the subject of the formula

                  E_D = \sqrt{\frac{2 * I_d}{c * \epsilon_o} }

substituting values

                 E_D = \sqrt{\frac{2 * 6.5*10^{-14}}{3.0*10^{8} * 8.85*10^{-12}} }

                       = 7*10^{-6} V/m

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                P_D = P_R

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                   = \frac{1}{2}  c \epsilon_o E_D^2  (\pi R^2)

And  P_R is the power incident on the dish which is mathematically represented as

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                \frac{1}{2}  c \epsilon_o E_D^2  (\pi R^2) =  \frac{1}{2} c \epsilon_o E_R^2 A_R

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                   R = \sqrt{\frac{E_R^2 A_R}{\pi E_D^2} }

Substituting values

                   R = \sqrt{\frac{(0.1 *10^{-3})^2 * 5}{\pi (7*10^{-6})^ 2} }

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