A sound wave of frequency f travels horizontally to the right. It is reflected from a large vertical plane surface moving to the left with a speed v. The speed of sound in the medium is c, then study following $$statements(i)$$ The frequency of the reflected wave is $$f(c+v)c$$−$$v(ii)$$ The wavelength of the reflected wave is $$c(c$$−$$v)f(c+v)(iii)$$ The number of waves striking the surface per second is $$f(c+v)c(iv)$$ The number of beats heard by a stationary listener to the left of the reflecting surface is fvc−vCorrect statements are

Question

A sound wave of frequency f travels horizontally to the right. It is reflected from a large vertical plane surface moving to the left with a speed v. The speed of sound in the medium is c, then study following $$statements(i)$$ The frequency of the reflected wave is $$f(c+v)c$$−$$v(ii)$$ The wavelength of the reflected wave is $$c(c$$−$$v)f(c+v)(iii)$$ The number of waves striking the surface per second is $$f(c+v)c(iv)$$ The number of beats heard by a stationary listener to the left of the reflecting surface is fvc−vCorrect statements are

Infinity Learn · Accepted Answer

Number of waves striking the surface per second (or$$ the frequency of the waves reaching surface of the moving $$target) n′$$=(c+v)$$λ$$=f(c+v)cNow$$ these waves are reflected by the moving $$target(Which$$ now act as a $$source)$$. Therefore apparent frequency of reflected second n′′$$=cc$$−vn′$$=fc+vc$$−vThe wavelength of reflected wave $$=cn$$′′$$=c(c$$−$$v)f(c+v)The$$ number of beats heard by stationary $$listener=n$$′′−$$f=fc+vc$$−v−$$f=2fv(c$$−$$v)Hence$$ option (a) is correct.

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