Question

Q|C The speed of a one-dimensional compressional wave traveling along a thin copper rod is 3.56 km/s . The rod is given a sharp hammer blow at one end. A listener at the far end of the rod hears the sound twice, transmitted through the metal and through air, with a time interval Δt between the two pulses.(d) Imagine that the copper rod is replaced by another material through which the speed of sound is v_r . What is the length of the rod in terms of t and v_r ?

Answer 1

The length of rod in terms v(r) and t is L = [  Δt / (1/343) - (1/v(r)) ].

3.56 km/s is the speed of a one-dimensional compressional wave moving along a thin copper rod.

At one end of the rod, a hard hammer strike is delivered. With a time interval of Δt between the two pulses, a listener at the other end of the rod hears the sound twice as it travels through the metal and the air.

The time interval is given by t = L/v.

The delay between pulses arrivals is:

Δt = L [(1/v(air)) - (1/v(copper))]

Now,

When the copper rod is swapped out for a different substance and the sound speed is measured as v(r).

The speed of air, v(air) = 343 m/s

Then,

L = [  Δt / (1/v(air)) - (1/v(r)) ]

L = [  Δt / (1/343) - (1/v(r)) ]

Here L is the length of the rod, Δt is in seconds and v(r) is the speed of sound in the rod.

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