A source S emitting sound of frequency 288 Hz is fixed on block B which is attached to the free end of a spring `S_(2)` and an observer O is on block A which is attached to the free end of spring `S_(1)` as shown in the figure. The blocks A and B are simultaneously displaced towards each other through a distance of 0.5 m and then left to oscillate. If the angular velocity of each blocks is `40"rad"s^(-1)`, then the maximum frequency observed by the observer is (speed of sound in air is 340 `ms^(-1)`)

Options

A. 288 Hz
B. 310 Hz
C. 324 Hz
D. 256 Hz

Answer

C

Explanation

Frequency is maximum, when both O and .S. are moving towards each other with maximum speeds.
Now, maximum speed of O = maximum speed of S
[and these two occur together].
`=v_(m)=aomega=0.5xx40=20ms^(-1)`
So, maximum frequency
= `f_(max)=f((v_("sound")+v_("observer"))/(v_("sound")-v_("observer")))=280xx((340+20)/(340-20))`
= 324 Hz