Two sources of sound A and B are moving towards and away from a stationary observer with the same speed respectively. If the frequency of the sound produced by both the sources is equal to 400 Hz , then the speed of sources (approximately) if the observer detects 4 beats per second, is [Given, speed of sound = 340 m s - 1 ]

Step-by-step solution

Given, frequency of sound produced by sources A and B , f A = f B = 400   Hz Speed of sound in air, v = 340   m   s - 1 Apparent frequency heard by the observer when source A is moving towards him, f A ' = v v - v S × f A = 340 340 - v S × 400 Apparent frequency heard by the observer when source B is moving away from him, f B ' = v v + v s × f B = 340 340 + v s × 400 Given, Beats = f A ' - f B ' = 4 340 340 - v s × 400 - 340 340 + v s × 400 = 4 ⇒ 34000 × 2 v S