A tall flagpole is a harmonic oscillator, flexing back and forth with a steady period. The pole rises from a base that is fixed
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First we need to find the speed of the dolphin sound wave in the water. We can use the following relationship between frequency and wavelength of a wave:
where
v is the wave speed
its wavelength
f its frequency
Using
and 
, we get
We know that the dolphin sound wave takes t=0.42 s to travel to the tuna and back to the dolphin. If we call L the distance between the tuna and the dolphin, the sound wave covers a distance of S=2 L in a time t=0.42 s, so we can write the basic relationship between space, time and velocity for a uniform motion as:
and since we know both v and t, we can find the distance L between the dolphin and the tuna:
where
v is the wave speed
f its frequency
Using
We know that the dolphin sound wave takes t=0.42 s to travel to the tuna and back to the dolphin. If we call L the distance between the tuna and the dolphin, the sound wave covers a distance of S=2 L in a time t=0.42 s, so we can write the basic relationship between space, time and velocity for a uniform motion as:
and since we know both v and t, we can find the distance L between the dolphin and the tuna: