The output potential difference (pd) of the signal generator is displayed on the oscilloscope, as shown in Figure 16 - AQA - A-Level Physics - Question 3 - 2019 - Paper 3

From Figure 17, we can observe that the stationary wave exhibits a pattern where the distance between two consecutive nodes is needed to calculate the wavelength.

The distance between nodes in this example is given as x, which we need to reference from the scale shown in Figure 17. Assuming x measures, for example, 20 cm for the full wavelength:

Thus, the wavelength is:

$ext{λ} = 2x = 2 imes 20 ext{ cm} = 40 ext{ cm} = 0.40 ext{ m}$

The speed c of the wave is calculated using the relationship:

$c = f imes ext{λ}$

Substituting our frequency calculated previously (50 Hz) and the wavelength (0.40 m):

$c = 50 ext{ Hz} imes 0.40 ext{ m} = 20 ext{ m s}^{-1}$

To determine the mass per unit length (μ), we may use the relationship for the frequency and speed of a wave:

ext{μ} = rac{c^2}{f^2}

Let's substitute the values:

μ = rac{20^2}{50^2} = rac{400}{2500} = 0.16 ext{ kg m}^{-1}

Using the readings from the digital calipers:

The readings from the left jaw are 0.62 mm and from the right jaw are 0.09 mm, thus:

$d = 0.62 ext{ mm} - 0.09 ext{ mm} = 0.53 ext{ mm}$

To limit random errors in measuring the diameter of the rod:

1. Take multiple measurements at different points along the diameter and calculate the average.
2. Ensure the calipers are calibrated properly before use.
3. Avoid parallax errors by keeping the eye level with the reading.
4. Use consistent pressure when closing the jaws of the calipers.

To determine the density, we need to use the mass and the volume relation: