The expression for the apparent frequency when the source is moving towards the observer is given by, n1=n0⋅
v
v−vs
The expression for the apparent frequency when the source is moving away from the observer is given by, n2=n0⋅
v
v+vs
The expression representing the beats heard by the observer is. x=n1−n2 =n0v[
1
v−vs
−
1
v+vs
] =n0v[
v+vs−v+vs
v2−vs2
] x(v2−vs2)=n0v(2vs) Further solving it as x(v2−vs2)=n0v(2vs) vs2+35000vs−122500=0 The roots of the above quadratic equation is calculated as, vs=