Read the following passage and answer the accompanying questions - Leaving Cert Physics - Question 11 - 2006

The frequency () of a stretched string is related to its tension (T) by the formula:

$f \propto \sqrt{T}$

This implies that as the tension increases, the frequency of vibration of the string also increases.

The speed of the wave (v) in the string can be calculated using the formula:

$v = f \times \lambda$

Where \lambda is the wavelength. For a string fixed at both ends, the wavelength of the fundamental frequency is \( \lambda = 2L \), where L is the length of the string.

Here, ( L = 0.8 m ), thus $\lambda = 2 \times 0.8 = 1.6 m$

Substituting into the speed formula:

$v = 400 \text{ Hz} \times 1.6 \\ m = 640 \text{ m/s}$.

The strings in an electric guitar must be made of steel because steel is a ferromagnetic material. This property allows the strings to be magnetised by the bar magnets placed beneath them, which is essential for inducing an electrical current when the strings vibrate.

Magnetic flux (Φ) is defined as the product of the magnetic field (B) and the area (A) through which the field lines pass, given by the formula:

$Φ = B \cdot A$

The unit of magnetic flux is the Weber (Wb).

The current produced in the coil of the electric guitar varies due to the amplitude of the vibrating string. As the string vibrates, it changes the magnetic flux through the coil, inducing an electromotive force (emf) according to Faraday's law of electromagnetic induction.

When the number of turns in the coil is increased, the induced electromotive force (emf) also increases, which leads to a higher (greater) signal output. This results in a louder sound or more intense sound output from the electric guitar.

The induced emf (E) in the coil can be calculated using Faraday's law of induction, given by:

$E = -N \frac{\Delta Φ}{\Delta t}$

Substituting the values:

• N = 5000 turns
• ( \Delta Φ = 8 \times 10^{-4} \text{ Wb} )
• ( \Delta t = 0.1 \text{ s} )

The calculation yields:

$E = -5000 \times \frac{8 \times 10^{-4}}{0.1} = -40 ext{ V}$