Question

1.A Radio station broadcasts modern song on medium wave 350 Hz every day at ten o’clock in the morning. The velocity of radio wave is 3X108 ms-1. The wavelength of another wave created in water is one percent of the radio wave and the velocity of sound in water is 1450 ms-1.

How many times of the frequency of the radio wave that of the wave created in the water? Analyze mathematically.

Answer 1

`ans \: = \boxed{{4.8 * 10}^( - 4) Hz}`

Step-by-step explanation:

`given \to \\ f_(r) = 350 \: \\ v_(r) = {3 * 10}^(8) \\ but \to \\ v = f \gamma \to \: \gamma = (v)/(f) : hence \to \\ \gamma _(r) = (v_(r))/(f_(r)) = (3 * 10^(8) )/(350) = \boxed{857,142.85714 \: m}\\ therefore \to \\ given \to \\ f_(w) = water \: frequency = \: \boxed{ ?}\: \\ v_(w) = 14 50 \\ but \to \\ v = f \gamma \to \: \gamma = (v)/(f) : hence \to \\ \gamma _(w) = (v_(w))/(f_(w)) = (1)/(100) * \gamma _(r) = (1)/(100) * 857,142.85714 \\\gamma _(w) = \boxed{8,571.4285714 \: m} : hence \to \: \\ f_(w) = (v_(w))/( \gamma _(w)) = (1450)/(8,571.4285714) = \boxed{0.1691666667} \\ if \: the \: number \: of \: times = \boxed{ x} \\ f_(r) (x)=f_(w) \\ (x) = (f_(w))/(f_(r)) = (0.1691666667)/(350) = 0.0004833333 \\ hence \to \\ the \: frequency \: of \: the \: radio \: wave \: is \to \: \boxed{{4.8 * 10}^( - 4) }\: \\ that \: of \: the \: wave \: created \: in \: the \: water.`

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