Sounds are produced when something vibrates - Leaving Cert Physics - Question d - 2021

To demonstrate resonance, we can use two tuning forks of the same natural frequency.

Apparatus:

• Two tuning forks of identical frequency.
• A resonating box (or a solid surface).

Procedure:

1. Strike one tuning fork to create vibrations.
2. Bring the second tuning fork close to the first tuning fork, without making direct contact.
3. Observe the second tuning fork start to vibrate and produce sound due to energy transfer from the first fork.

Conclusion:

This experiment illustrates resonance, where one tuning fork vibrates at the same natural frequency as the other.

The frequency of a stretched string is inversely proportional to its length. Mathematically, this can be expressed as:

$f \propto \frac{1}{L}$

where $f$ is the frequency and $L$ is the length of the string.

Given the wave speed $v = 380 \, \text{m/s}$ and using the relationship:

$v = f \lambda$

We need to calculate the wavelength $\lambda$. First, we need to find the frequency using the distance between adjacent nodes:

Calculating frequency:

The distance between two adjacent nodes is half of the wavelength:

$\lambda = 2 \times 40 \text{ cm} = 80 \text{ cm} = 0.80 \text{ m}$

Now substituting back:

$f = \frac{v}{\lambda} = \frac{380 \, \text{m/s}}{0.80 \, \text{m}} = 475 \, \text{Hz}$

Therefore, the wavelength is $0.80$ m.

The frequency of the wave, as previously calculated, is $f = 475 \, \text{Hz}$.