Question

1. A guitar is an excellent example of standing waves on strings. If you tighten a guitar string, what effect will it have on the frequency of the note it produces when strummed? Explain in terms of our formula, f2= FTensionμλ2

2. When a guitar player uses their finger to pin down the string somewhere on the neck of the guitar, the frequency of the note the string produces also changes. Explain why this change might occur, in terms of our formula, f2= FTensionμλ2

3. Does linear density have a role in the frequency of guitar strings? Explain what effect increasing linear density of a string may have on the frequency of the note and relate that to our formula, f2= FTensionμλ2

Answer 1

1. When a guitar string is tighened, the tension in the string increases. Hence frequency of the note also increases.

If f1 is the initial frequency when the tension in the string is F1 and the wavelength is λ1, then by the formula,

   f1 = ( F1/μ)1/2 /λ1,    ...eq(1)

As the F1 i.e. tension increases, frequency of the node also increases.

2. The standing waves are produced in guitar strings when the following condition is satisfied,

   L = (n λ ) / 2    ...eq(2)

where L is the length of the string and λ is the wavelength of the note, n being an integer.

When the guitarist pins somewhere on the neck of the guitar, it creates a node there i.e. n ( mode of vibration) is changed. L being constant, according to eq(2), wavelength of the note i.e. λ changes. Then according to eq(1), frequency of the note also changes, as the frequency is inversly proportional to wavelength.

3. μ is the linear density of the guitar string. If the linear density of the string is increased, then the frequency of the note decreases as according to eq (1), the frequency is inversly proportional to the square root of the linear density of the string.