Question: A seismologist records earthquake wave amplitudes every 4 seconds. If one seismic event lasts 6 minutes, how many data points are recorded during the entire event? - Sourci

Understanding the Context

Calculating the Duration in Seconds
The event lasts 6 minutes. Convert this to seconds:
6 minutes × 60 seconds/minute = 360 seconds

Determining the Number of Data Points
Since data is recorded every 4 seconds, divide the total duration by the sampling interval:
360 seconds ÷ 4 seconds/data point = 90 data points

However, because data collection begins at time zero (the first reading), and the event lasts exactly 360 seconds, we include the initial data point. Thus, the total number of recorded data points is 90 + 1 = 91. But in many technical contexts—especially when analyzing continuous signals—the offset is minimized by strict intervals, leading commonly to:
360 ÷ 4 = 90 data intervals, with the first at 0 seconds, so 90 + 1 = 91, or simply 90 data points when counting discrete samples.

To clarify:

• If sampling starts at t = 0 and continues at t = 4, 8, ..., up to t = 356 or 360, the number depends on whether endpoint inclusion is counted.
  
• In seismic data logging, [0 to T] inclusive at 4-second intervals yields:
  360 ÷ 4 + 1 = 91 points, but if the event ends exactly at the final interval, often the count is adjusted to 90 or 91 depending on protocols.

Key Insights

For most practical purposes in seismic analysis—especially in educational and research reporting—if a wave is recorded every 4 seconds starting at 0, the number of data points over 360 seconds is:

✅ 90 data points, assuming the initial reading is taken at t = 0 and subsequent readings follow every 4 seconds, with the last one recorded at t = 356 seconds (since 360 is not a multiple of 4), giving:
0, 4, 8, ..., 356 → This is an arithmetic sequence with:
First term = 0, common difference = 4, last term = 356
Number of terms: n = (356 – 0)/4 + 1 = 89 + 1 = 90

Why This Matters
Accurately counting data points ensures proper analysis of wave characteristics like amplitude decay, frequency shifts, and phase arrival times. These metrics help seismologists determine earthquake magnitude, depth, and potential risks.

Conclusion
A seismologist recording earthquake wave amplitudes every 4 seconds during a 6-minute (360-second) event captures 90 discrete data points when sampling begins at the start and proceeds at consistent intervals. Proper understanding of time-stamped data collection is essential for reliable seismic monitoring and disaster preparedness.

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Keywords: seismologist data collection, earthquake wave amplitudes, seismic monitoring, data point calculation, 4-second sampling rate, earthquake duration analysis, real-time seismic recording, waveform data

Final Thoughts

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