Question

The velocity of the transverse waves produced by an earthquake is 5.05 km/s, while that of the longitudinal waves is 8.585 km/s. A seismograph records the arrival of the transverse waves 56.4 s after that of the longitudinal waves. How far away was the earthquake? Answer in units of km.

Answer 1

`d=691.71km`

Step-by-step explanation:

The time lag between the arrival of transverse waves and the arrival of the longitudinal waves is defined as:

`t=(d)/(v_t)-(d)/(v_l)`

Here d is the distance at which the earthquake take place and
`v_t, v_l` is the velocity of the transverse waves and longitudinal waves respectively. Solving for d:

`t=d((1)/(v_t)-(1)/(v_l))\\d=(t)/((1)/(v_t)-(1)/(v_l))\\d=(56.4s)/((1)/(5.05(km)/(s))-(1)/(8.585(km)/(s)))\\d=691.71km`