A heavy ball of mass $M$ is suspended from the ceiling of a car by a light string of mass $m$ $(m < < M).$ When the car is at rest, the speed of transverse waves in the string is $60\;m{s^{ - 1}}.$ When the car has acceleration a, the wave speed increases to $60.5\;m{s^{ - 1}}.$ The value of a, in terms of gravitational acceleration $g$ is closest to