What Is the Vibrational Frequency of a Guitar String Based on Beat Frequencies?

[Malicious]

Homework Statement

A guitar string produces 4 beat/s when sounded with a 350-Hz tuning fork and 9 beat/s when sounded with a 355-Hz fork. What is the vibrational frequency of the string? Explain your reasoning.

Homework Equations

f=v//\

The Attempt at a Solution

I'm not quite sure how to start solving this problem. I know that frequency is velocity divided by wavelength. What equation or equations that have beat/s as variables could I use to solve this problem?

 

[andrevdh]

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html"

More info appears lower down on the page by scrolling down.

 

[m2003]

I would approach this problem by first understanding the concept of vibrational frequency. Vibrational frequency refers to the number of complete oscillations or cycles a vibrating object undergoes in a given unit of time. In this case, the vibrating object is the guitar string and the unit of time is one second.

Next, I would use the given information to set up a mathematical relationship between the frequency of the tuning forks and the number of beats produced. The fact that the string produces 4 beats per second with a 350-Hz fork and 9 beats per second with a 355-Hz fork tells us that there is a difference of 5 beats per second between the two frequencies.

Using the formula for beat frequency, which is the difference between the frequencies of two waves, I can set up the following equation:

Beat frequency = |f1 - f2| = 5 beat/s

Where f1 is the frequency of the 350-Hz tuning fork and f2 is the frequency of the 355-Hz tuning fork.

Solving for the unknown, we get:

|f1 - f2| = 5 beat/s
|350 Hz - 355 Hz| = 5 beat/s
5 Hz = 5 beat/s

Therefore, the vibrational frequency of the string is 5 Hz. This means that the string undergoes 5 complete oscillations per second when it is sounded with the tuning forks.

In summary, the concept of vibrational frequency, along with the formula for beat frequency, can be used to solve this problem. By understanding the relationship between frequency and the number of beats produced, we can determine the vibrational frequency of the guitar string.