A man strikes one end of a thin rod with a hammer. The speed of sound in the rod is 19 times the speed of sound in air. A woman, at the other end with her ear close to the rod, hears the sound of the blow twice with a 0.19 s interval between; one sound comes through the rod and the other comes through the air alongside the rod. If the speed of sound in air is 347 m/s, what is the length of the rod

69.6m

Explanation: Given that:

∆t = 0.19s

V.air = 347m/s

V.rod = 19×V.air

Also note that both sound covers the same distance both in two different medium.

Let us assume that x is the length of the rod, and the time it takes for sound in air to travel that distance is:

tₐ = x / 347

The time it takes for sound to travel through the rod is:

t = x / (19 × 347)

The difference between these is 0.19s:

tₐ - t = 0.19

x / 347 - x / (19 × 347) = 0.19

6593x-347x/2287771 = 0.19

6246x = 434676.49

x = 434676.49/6246

x = 69.59m

x = 69.6m

the total distance traveled by the car is

30km + 49km = 79 km .