Mechanical Waves require a medium to travel through in order to transport their energy from one location to another.
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Complete Question
A parallel plate capacitor creates a uniform electric field of 5 x 10^4 N/C and its plates are separated by 2 x 10^{-3}'m. A proton is placed at rest next to the positive plate and then released and moves toward the negative plate. When the proton arrives at the negative plate, what is its speed?
Answer:
![V=1.4*10^5m/s](https://tex.z-dn.net/?f=V%3D1.4%2A10%5E5m%2Fs)
Explanation:
From the question we are told that:
Electric field ![B=1.5*10N/C](https://tex.z-dn.net/?f=B%3D1.5%2A10N%2FC)
Distance ![d=2 x 10^{-3}](https://tex.z-dn.net/?f=d%3D2%20x%2010%5E%7B-3%7D)
At negative plate
Generally the equation for Velocity is mathematically given by
![V^2=2as](https://tex.z-dn.net/?f=V%5E2%3D2as)
Therefore
![V^2=\frac{2*e_0E*d}{m}](https://tex.z-dn.net/?f=V%5E2%3D%5Cfrac%7B2%2Ae_0E%2Ad%7D%7Bm%7D)
![V^2=\frac{2*1.6*10^{-19}(5*10^4)*2 * 10^{-3}}{1.67*10^{-28}}](https://tex.z-dn.net/?f=V%5E2%3D%5Cfrac%7B2%2A1.6%2A10%5E%7B-19%7D%285%2A10%5E4%29%2A2%20%2A%2010%5E%7B-3%7D%7D%7B1.67%2A10%5E%7B-28%7D%7D)
![V=\sqrt{19.2*10^9}](https://tex.z-dn.net/?f=V%3D%5Csqrt%7B19.2%2A10%5E9%7D)
![V=1.4*10^5m/s](https://tex.z-dn.net/?f=V%3D1.4%2A10%5E5m%2Fs)
Answer:
(a) The ratio of the pressure amplitude of the waves is 43.21
(b) The ratio of the intensities of the waves is 0.000535
Explanation:
Given;
density of gas,
= 2.27 kg/m³
density of liquid,
= 972 kg/m³
speed of sound in gas,
= 376 m/s
speed of sound in liquid,
= 1640 m/s
The of the sound wave is given by;
![I = \frac{P_o^2}{2 \rho C} \\\\P_o^2 = 2 \rho C I\\\\p_o = \sqrt{2 \rho CI}](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7BP_o%5E2%7D%7B2%20%5Crho%20C%7D%20%5C%5C%5C%5CP_o%5E2%20%3D%202%20%5Crho%20C%20I%5C%5C%5C%5Cp_o%20%3D%20%5Csqrt%7B2%20%5Crho%20CI%7D)
Where;
is the pressure amplitude
![P_o_g= \sqrt{2 \rho _g C_gI} -------(1)\\\\P_o_l= \sqrt{2 \rho _l C_lI}---------(2)\\\\\frac{P_o_l}{P_o_g} = \frac{\sqrt{2 \rho _l C_lI}}{\sqrt{2 \rho _g C_gI}} \\\\\frac{P_o_l}{P_o_g} = \sqrt{\frac{2 \rho _l C_lI}{2 \rho _g C_gI} }\\\\ \frac{P_o_l}{P_o_g} = \sqrt{\frac{ \rho _l C_l}{ \rho _g C_g} }\\\\ \frac{P_o_l}{P_o_g} = \sqrt{\frac{ (972)( 1640)}{ (2.27)( 376)} }\\\\\frac{P_o_l}{P_o_g} = 43.21](https://tex.z-dn.net/?f=P_o_g%3D%20%5Csqrt%7B2%20%5Crho%20_g%20C_gI%7D%20-------%281%29%5C%5C%5C%5CP_o_l%3D%20%5Csqrt%7B2%20%5Crho%20_l%20C_lI%7D---------%282%29%5C%5C%5C%5C%5Cfrac%7BP_o_l%7D%7BP_o_g%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B2%20%5Crho%20_l%20C_lI%7D%7D%7B%5Csqrt%7B2%20%5Crho%20_g%20C_gI%7D%7D%20%5C%5C%5C%5C%5Cfrac%7BP_o_l%7D%7BP_o_g%7D%20%3D%20%5Csqrt%7B%5Cfrac%7B2%20%5Crho%20_l%20C_lI%7D%7B2%20%5Crho%20_g%20C_gI%7D%20%7D%5C%5C%5C%5C%20%5Cfrac%7BP_o_l%7D%7BP_o_g%7D%20%3D%20%5Csqrt%7B%5Cfrac%7B%20%5Crho%20_l%20C_l%7D%7B%20%5Crho%20_g%20C_g%7D%20%7D%5C%5C%5C%5C%20%5Cfrac%7BP_o_l%7D%7BP_o_g%7D%20%3D%20%5Csqrt%7B%5Cfrac%7B%20%28972%29%28%201640%29%7D%7B%20%282.27%29%28%20376%29%7D%20%7D%5C%5C%5C%5C%5Cfrac%7BP_o_l%7D%7BP_o_g%7D%20%3D%2043.21)
(b) when the pressure amplitudes are equal, the ratio of the intensities is given as;
![I = \frac{P_o^2}{2 \rho C}\\\\I_g = \frac{P_o^2}{2 \rho _g C_g}-------(1)\\\\I_l = \frac{P_o^2}{2 \rho _l C_l}-------(2)\\\\\frac{I_l}{I_g} = (\frac{P_o^2}{2 \rho _l C_l})*(\frac{2\rho_gC_g}{P_o^2} )\\\\\frac{I_l}{I_g} = \frac{\rho _gC_g}{\rho_lC_l} \\\\\frac{I_l}{I_g} = \frac{(2.27)(376)}{(972)(1640)}\\\\ \frac{I_l}{I_g} = 0.000535](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7BP_o%5E2%7D%7B2%20%5Crho%20C%7D%5C%5C%5C%5CI_g%20%3D%20%5Cfrac%7BP_o%5E2%7D%7B2%20%5Crho%20_g%20C_g%7D-------%281%29%5C%5C%5C%5CI_l%20%3D%20%5Cfrac%7BP_o%5E2%7D%7B2%20%5Crho%20_l%20C_l%7D-------%282%29%5C%5C%5C%5C%5Cfrac%7BI_l%7D%7BI_g%7D%20%3D%20%28%5Cfrac%7BP_o%5E2%7D%7B2%20%5Crho%20_l%20C_l%7D%29%2A%28%5Cfrac%7B2%5Crho_gC_g%7D%7BP_o%5E2%7D%20%29%5C%5C%5C%5C%5Cfrac%7BI_l%7D%7BI_g%7D%20%3D%20%5Cfrac%7B%5Crho%20_gC_g%7D%7B%5Crho_lC_l%7D%20%5C%5C%5C%5C%5Cfrac%7BI_l%7D%7BI_g%7D%20%3D%20%5Cfrac%7B%282.27%29%28376%29%7D%7B%28972%29%281640%29%7D%5C%5C%5C%5C%20%5Cfrac%7BI_l%7D%7BI_g%7D%20%3D%200.000535)
Gamma rays are the highest energy EM radiation and typically have energies greater than 100 keV, frequencies greater than 1019 Hz, and wavelengths less than 10 picometers.