Question

When an earthquake occurs, two types of sound waves are generated and travel through the earth. The primary, or P, wave has a speed of about 8.0 km/s and the secondary, or S, wave has a speed of about 4.5 km/s. A seismograph, located some distance away, records the arrival of the P wave and then, 77.2 s later, records the arrival of the S wave. Assuming that the waves travel in a straight line, how far (in terms of m) is the seismograph from the earthquake?

Answer 1

To calculate the distance to the earthquake's epicenter, we use the time difference between the arrival of P-waves and S-waves and their speeds. By setting up an equation and solving for the distance, the seismograph is found to be approximately 618,940 meters from the epicenter.

Step-by-step explanation:

When an earthquake occurs, two types of waves are generated: P-waves (primary waves) and S-waves (secondary waves), each with distinctive speeds. To determine the distance to the epicenter of the earthquake, we use the formula d = v × t, where d is distance, v is velocity, and t is time. Given that the P-wave has a speed of 8.0 km/s and the S-wave has a speed of 4.5 km/s, and the time difference of arrival between the two waves is 77.2 seconds, we can calculate the distance from the seismograph to the earthquake's epicenter.

Let the distance be d, then:

• Time for P-wave to travel d: d / 8.0 km/s
• Time for S-wave to travel d: d / 4.5 km/s
• The difference in travel time is 77.2 s, so: d / 4.5 km/s - d / 8.0 km/s = 77.2 s

To find the distance d, we solve the equation:

1. 8.0×d - 4.5×d = 77.2 s × (8.0 km/s × 4.5 km/s)
2. 3.5×d = 77.2 s × 36 km²/s²
3. d ≈ 618.94 km

Now, to convert kilometers to meters:

• d ≈ 618.94 km × 1,000 m/km
• d ≈ 618,940 m

Therefore, the seismograph is approximately 618,940 meters from the earthquake's epicenter.

Answer 2

Answer:
`d=7.94* 10^5\ m`

Step-by-step explanation:

Given

Speed of Primary wave
`v_1=8\ km/s`

Speed of secondary wave
`v_2=4.5\ km/s`

difference in timing of two waves are
`77.2\ s`

Suppose both travel a distance of d km then

`t_1=(d)/(8)\quad \ldots (i)`

`t_2=(d)/(4.5)\quad \ldots (ii)`

Subtract (ii) from (i)

`(d)/(4.5)-(d)/(8)=77.2`

`d[(1)/(4.5)-(1)/(8)]=77.2`

`d[0.0972]=77.2`

`d=794.23\ km`

`d=7.94* 10^5\ m`