Musical instruments produce stationary (standing) waves - Leaving Cert Physics - Question 9 - 2015

Resonance is the transfer of energy between two bodies that have the same or similar natural frequency.

Laboratory Experiment to Demonstrate Resonance:

• Apparatus: Tuning fork, resonating box, and damping medium.
• Method: Strike the tuning fork and hold it over the resonance box. Adjust the position until the sound is maximized. This occurs due to the matching frequencies causing greater amplitude vibrations.
• Observation: The sound becomes significantly louder during resonance compared to when the tuning fork is away from the box.

1. Length of the string
2. Mass per unit length (linear density) of the string.

The frequency increases. The relationship can be expressed by the formula:

A pipe open at both ends supports both odd and even harmonics, while a pipe open at one end supports only odd harmonics due to the boundary conditions.

Diagrams:

1. First harmonic for open pipe: Shows fundamental frequency with nodes at both ends.
2. First harmonic for closed pipe: Shows only one node at the closed end, and antinode at the open end.
3. All harmonics for open pipe: Includes all harmonics.
4. Only odd harmonics for closed pipe: Includes half; the first harmonic is the only even harmonic.

To find the length of the pipe, the wave speed can be used: v = fλ. Given that the fundamental frequency is 587 Hz and speed of sound is 340 m/s, the wavelength (λ) can be calculated as: $λ = \frac{v}{f} = \frac{340 m/s}{587 Hz} ≈ 0.58 m$ For a closed pipe, length (L) is given as: $L = \frac{λ}{4} ≈ 0.58 m / 4 ≈ 0.145 m$.