Determine the length of a copper pipe if the sound from a blow at one end of the pipe is heard at the other twice with an interval of 0.9 s. The speed of sound in air is 340 m / s, and in copper 3400 m / s
Δt = 0.9 s.
Vv = 340 m / s.
Vm = 3400 m / s.
Sound is a mechanical wave that travels through the air and copper pipe.
Since the speed of sound propagation in copper Vm is greater than in air Vv, sound propagates through a copper pipe earlier than through air. Therefore, the sound from the impact is heard twice.
Δt = tv – tm, where tv is the propagation time of sound from a shock in the air, tm is the propagation time of sound from a shock in a copper pipe.
tv = S / Vv, tm = S / Vm, where S is the length of the pipe.
Δt = S / Vv – S / Vm = S * (Vm – Vv) / Vw * Vm.
S = Vv * Vm * Δt / (Vm – Vv).
S = 340 m / s * 3400 m / s * 0.9 s / (3400 m / s – 340 m / s) = 377.8 m.
Answer: a copper pipe has a length of S = 377.8 m.
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