Stationary Waves on a String

Equipment

• Signal generator: To create the frequency needed to induce waves on the string.
• Vibration generator: Connects to the string to produce vibrations.
• Stand and pulley system: To support the string and apply tension.
• Wooden bridge: To adjust the length of the vibrating section of the string.
• 100g masses with holder: To create tension in the string (9.81 N when using 100g).
• Metre ruler: To measure the vibrating length of the string.
• $1.5$m long string: Used to produce the waves.
• Balance: To measure the mass of the string for calculating mass per unit length.

Graphs and Calculations

1. Plotting Frequency vs. Inverse Length:

• Plot the mean frequency $f$ against $\frac{1}{l}$.
• Draw a line of best fit to determine the gradient $G$.
• The wave speed $v$ on the string can be calculated as:

$$v = 2 \times G$$

2. Wave Speed Calculation:

• Using the first harmonic condition where wavelength $\lambda = 2l$:

$$v = f \lambda = 2f \cdot l$$

• This implies that the wave speed $v = 2 \times \text{gradient}$.

3. Tension Calculation:

• The tension $T$ in the string is due to the weight of the hanging mass:

$$T = mg$$

• Here, if using a 100g mass, $T = 0.100 \text{ kg} \times 9.81 \text{ m/s}^2 = :highlight[0.981 N]$.

4. Alternative Calculation of Wave Speed:

• Using the relationship:

$$v = \sqrt{\frac{T}{\mu}}$$

• Compare this theoretical value of $v$ with the one obtained from the gradient.

Improvements and Notes

1. Further Testing:

• Vary Mass: Repeat the experiment with different masses to observe the effect of tension on wave frequency.
• Change String Thickness: Use strings of different thicknesses to see how mass per unit length affects wave behaviour.

2. Using an Oscilloscope:

• Connect an oscilloscope to verify the signal generator's output frequency, ensuring accuracy.

3. Allow Stabilisation:

• Wait approximately 20 minutes for the signal generator to stabilise for consistent results.