Final answer:
To produce a beat frequency of 4 Hz with a 256 Hz tuning fork and a guitar, tune the guitar string to either 260 Hz or 252 Hz, causing the frequencies to differ by 4 Hz, resulting in the desired beat frequency.
Step-by-step explanation:
To produce a beat frequency of 4 Hz using a 256 Hz tuning fork and a guitar, you would need to adjust one of the guitar strings to vibrate either slightly faster or slightly slower than the tuning fork. If the tuning fork vibrates at 256 Hz, then you would need to tune the guitar string to vibrate at either 260 Hz or 252 Hz. If the string vibrates at 260 Hz, the beat frequency would be 260 Hz - 256 Hz = 4 Hz. Similarly, if the string vibrates at 252 Hz, the beat frequency would be 256 Hz - 252 Hz = 4 Hz. Adjusting the string tension and thereby changing its frequency can achieve this effect. Piano tuners and other musicians often use this phenomenon of beats to tune their instruments with precision.