When a guitar string is sounded along with a 440Hz tuning fork, a beat frequency of 5Hz is heard. When the same string is sounded along with a 43Hz tuning fork, the beat frequency is 9Hz. What is the frequency of the string??.. The first thing i thought of doing was putting both sets of values in the fb=abs.f2-f1 formula, but thing is, i don't know what to do when once i have acquired 2 different values for the frequency of the string?

Question

When a guitar string is sounded along with a 440Hz tuning fork, a beat frequency of 5Hz is heard. When the same string is sounded along with a 43Hz tuning fork, the beat frequency is 9Hz. What is the frequency of the string??.. The first thing i thought of doing was putting both sets of values in the fb=abs.f2-f1 formula, but thing is, i don't know what to do when once i have acquired 2 different values for the frequency of the string?

Answer 1

Are you sure the 43 Hz tuning fork frequency is not a typing error? You can't get a 9 Hz beat frequency with that.

Answer 2

the second fork is probably 436 Hz

Answer 3

To find the frequency of the guitar string, we can start by setting up two equations based on the given information.

Let's assume the frequency of the guitar string is denoted by f. We are given that when the guitar string is sounded along with a 440Hz tuning fork, a beat frequency of 5Hz is heard. This means that the difference between the frequency of the guitar string and the tuning fork is 5Hz. So, we can write the first equation as:

|f - 440Hz| = 5Hz (Equation 1)

Similarly, when the guitar string is sounded along with a 43Hz tuning fork, a beat frequency of 9Hz is heard. This implies that the difference between the frequency of the guitar string and the tuning fork is 9Hz. We can express this as the second equation:

|f - 43Hz| = 9Hz (Equation 2)

To solve these equations, we need to consider both cases when the expression inside the absolute value signs is positive and negative. Let's consider the positive cases:

For Equation 1:
f - 440Hz = 5Hz
f = 445Hz

For Equation 2:
f - 43Hz = 9Hz
f = 52Hz

So, we have two possible frequencies for the guitar string: 445Hz and 52Hz.

To determine the correct frequency, we need to consider the relationship between the beat frequency and the frequency of the string. The beat frequency is the difference between the frequencies of the tuning fork and the string. Therefore, the beat frequency is always positive. In this case, we have a beat frequency of 5Hz when the string is sounded with a 440Hz tuning fork and a beat frequency of 9Hz when sounded with a 43Hz tuning fork.

Since the beat frequency is determined by the difference between the two frequencies, we need to choose the frequency of the string that will give us the correct beat frequencies.

Therefore, the frequency of the guitar string is 445Hz.