A highway truck has two horns A and B. When sounded together, the driver records 50 beats in 10 seconds. With horn B blowing and the truck moving towards a wall at a speed of 10 m/s, the driver noticed a beat frequency of 5 Hz with the echo. When frequency of A is decreased the beat frequency with two horns sounded together increases. Calculate the frequency of horn A. (Speed of sound in air = 330 m/s)

Options

A. 75 Hz
B. 85 Hz
C. 90 Hz
D. 95 Hz

Answer

A

Explanation

Here, let frequencies of horn A and B are `n_(A)` and `n_(B)`, respectively.
As given, `n_(A)-n_(B)=50/10`
`n_(A)-n_(B)=5` beats
When, the horn B is blown while moving towards the wall the apparent frequency,
`n_(B)'=n_(B) (v+v_(0))/(v-v_(s))`
Since, both the observer ans source are moving with truck.
So, `v_(s)=v_(o)=10` m/s
`n_(B)'=n_(B)((330+10)/(330-10))`
`n_(B)'=n_(B)1.0625`
`= n_(B)'-n_(B)=0.0625 n_(B)` As given, `n_(B)'-n_(B)=5`
`0.0625 n_(B)=5`
`n_(B)=80` Hz
`:'` Given, that if frequency of A is decreased then beat frequency of A is decreased then beat frequency is increases.
so, `n_(B) gt n_(A)`
`:. n_(A)=n_(B)-5=80-5`
`implies n_(A)=75` Hz