The frequency of a source of sound is f. A sound wave from this source is moving horizontally twoards right. The wave is reflected from a large vertical plane moving towards left with a speed v. The speed of sound in medium is C. Find the (a) number of waves striking the surface per second. (b) Wavelength and frequency of reflected wave. (c) beat frequency.

The frequency of a source of sound is f. A sound wave from this source

1.	The frequency of a source of sound is f. A sound wave from this source is moving horizontally twoards right. The wave is reflected from a large vertical plane moving towards left with a speed v. The speed of sound in medium is C. Find the (a) number of waves striking the surface per second. (b) Wavelength and frequency of reflected wave. (c) beat frequency.
Answer» Solution :f = original frequency of source of sound. The speed of sound in medium = C (a) NUMBER of waves encountered by vertical PLANE per unit TIME = frequency = f. = `("distance travelled/sec.")/("wavelength")` `= (C + upsilon)/(LAMBDA) = (C)/(lambda) (1 + (upsilon)/(C))` Let the wave is reflected from a vertical plane and is received by an observer at rest. (b) Let f.. = frequency of wave reflected by plane `f.. = (1)/(1 - (upsilon)/(C)) f.` `= (f ((C + upsilon)/(C)))/(1 - (upsilon)/(C)) = (f (1 + (upsilon)/(C)))/((1 - (upsilon)/(C)))` `f.. = (f(C + upsilon))/((C - upsilon))` `lambda.. = (C)/(f..) = (C (C - upsilon))/(f(C + upsilon))` Beat frequency = f.. - f `= (f(C + upsilon))/((C - upsilon)) - f` `= f ((C+upsilon)/(C - upsilon) - 1)` `= f((C + upsilon - C + upsilon)/(C - upsilon)) = (2 v f)/(C - upsilon)`