(i) A source of sound emits waves of frequency `f_(0) = 1200 Hz`. The source is travelling at a speed of `v_(1) = 30 m//s` towards east. There is a large reflecting surface in front of the source which is travelling at a velocity of `v_(2) = 60 m//s` towards west. Speed of sound in air is `v = 330 m//s`.
(a) Find the number of waves arriving per second at the reflecting surface.
(b) Find the ratio of wavelength `(lambda_(1))` of sound in front of the source travelling towards the reflecting surface to the wavelength `(lambda_(2))` of sound in front of the source approaching it after getting reflected.
(ii) A sound source (S) and an observer (A) are moving towards a point O along two straight lines making an angle of `60^(@)` with each other. The velocities of S and A are `18 ms^( –1)` and `12 ms^( –1)` respectively and remain constant with time. Frequency of the source is `1000 Hz` and speed of sound is `v = 330 ms^( –1)`.
(a) Find the frequency received by the observer when both the source and observer are at a distance of 180 m from point O (see figure). (b) Find the frequency received by the observer when she reaches point O.

Answer

(i) (a) 1560
(b) `13/ 9`
(ii) (a) 1047 Hz
(b) 991 Hz