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 cycles415 cycles600 cycles

1. Break Down the Problem

We need to calculate how many cycles the E-string completes within a given time (5.0 seconds) using its frequency (83 Hz).

2. Relevant Concepts

The frequency of a wave is defined as the number of cycles it completes per second. It is given by the formula: $\text{Total cycles} = \text{Frequency (Hz)} \times \text{Time (s)}$

3. Analysis and Detail

Given:

• Frequency $f = 83 \, \text{Hz}$
• Time $t = 5.0 \, \text{s}$

Using the formula: $\text{Total cycles} = 83 \, \text{Hz} \times 5.0 \, \text{s}$ Calculating this: $\text{Total cycles} = 415 \, \text{cycles}$

4. Verify and Summarize

The calculation seems correct since:

• $83 \times 5 = 415$

Final Answer

The E-string completes 415 cycles in 5.0 seconds.