Two sources A and B are sending notes of frequency 680 ~Hz . A listener moves from A and B with a constant velocity u . If the speed of sound in air is 340 ~ms ⁻¹ , what must be the value of u so that he hears 10 beats per second?

Step-by-step solution

Listener go from A B with velocity (u) let the apparent frequency of sound from source A by listener or aligned n^ & =n ( v-v_o v+v_s ) n^ & =680 ( 340-u 340+0 ) aligned The apparent frequency of sound from source B by listener aligned n^ & =n ( v+v_o v-v_s ) & =680 ( 340+u 340-0 ) aligned But listener hear 10 beats per second. Hence, n^ -n^ =10 or 680 ( 340+u 340 )-680 ( 340-u 340 )=10 or aligned or 2(340+u-340+u) & =10 or u=2.5 ~m ~s ⁻¹ aligned