The correct option is A 1.5 m/s
Given,
Velocity of sound, v=340 m/s
Natural frequency of tuning fork, f0=340 Hz
Let,
f1= frequency observed by observer due to fork 1,
f2= frequency observed by observer due to fork 2,
vs= velocity of tuning fork,
As we know that,
f1=f0(vv−vs) and
f2=f0(vv+vs)
According to the problem, the beat frequency,
f1−f2=3
Substituting the values we get,
f0(vv−vs)−f0(vv+vs)=3
⇒⎡⎢
⎢⎣1(1−vsv)−11+vsv⎤⎥
⎥⎦f0=3
⇒[(1−vsv)−1−(1+vsv)−1]f0=3
By binomial expansion with neglecting higher terms,
⇒[(1+vsv)−(1−vsv)]f0=3
⇒2vsf0v=3
⇒vs=3v2f0
Substituting the values, we get
vs=(3)(340)(2)(340)=1.5 m/s
Hence, correct option is (a).