One end of a steel bridge is struck by a hammer. the sound produced is transmitted through the bridge and through the air to the other side of the bridge. there is a 1.4 s delay between the arrivals of the two sounds. what is the length of the bridge if the velocity of sound in air is 340 m/s and in steel is 5100 m/s. m

The sound in steel covers the distance L (length of the bridge) in a time , with a velocity :

which we can rewrite as
(1)

Similarly, the sound in air covers the length of the bridge L in a time , with a velocity :

which we can rewrite as
(2)
We also know that the sound in air arrives with a delay of 1.4 s. This means we can rewrite tA as
(3)

The length of the bridge is always the same, so we can write (1)=(2) and using the information found in (3):

Re-arranging, we find


And at this point we can find the length of the bridge: