The open E-string on a guitar vibrates with a frequency of 83 Hz. How many cycles does it complete in 5.0 s? *1 point78 cycles88 cycl

1. Break Down the Problem

To find the total number of cycles completed by the E-string in 5.0 seconds, we need to utilize the frequency of the string and the time duration.

2. Relevant Concepts

The formula to find the number of cycles (N) completed over a certain time (t) when the frequency (f) is known is: $N = f \times t$

3. Analysis and Detail

1. Given:

   • Frequency (f) = 83 Hz
   • Time (t) = 5.0 s

2. Substitute the values into the formula: $N = 83 \text{ Hz} \times 5.0 \text{ s}$

3. Calculate: $N = 415 \text{ cycles}$

4. Verify and Summarize

The calculation shows that the E-string vibrates 415 cycles in 5.0 seconds.

Final Answer

415 cycles.