A Level Physics Practice Exam

How can a guitarist increase the fundamental frequency of his strings?

1. Decrease the length of the string

2. Increase the tension in the string

3. Decrease the mass of the string

4. Change the material of the string

The correct answer is: Increase the tension in the string

The correct method for a guitarist to increase the fundamental frequency of the strings is to increase the tension in the string. In stringed instruments, the fundamental frequency is determined by several factors, specifically the tension of the string, its length, and its mass per unit length. The equation that relates these factors is given by: \( f = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \) where \( f \) is the fundamental frequency, \( L \) is the length of the string, \( T \) is the tension in the string, and \( \mu \) is the mass per unit length of the string. Increasing the tension \( T \) in the equation directly leads to an increase in frequency \( f \). This means that the higher the tension on the string, the higher the pitch of the note it produces. While decreasing the length of the string and decreasing the mass can also lead to a higher frequency, these methods are not as straightforward or practical for adjustments by a guitarist. Changing the material of the string may affect the sound quality and vibrational properties, but it does not provide a direct way to increase frequency in the same clear manner as increasing tension does.