Question

(a) One end of a plastic foot ruler is held tightly at the edge of a table and the other end is plucked. Name the vibrations produced in the ruler.
(b) Now the ruler is pushed inside partially and plucked again from its free end. State with a reason whether the frequency of vibration increases or decreases.

Hint:

For vibrating strings or rulers, remember this simple rule: shorter length = higher frequency = higher pitch/shriller sound.

Answer 1

Step 1: Understanding the Concept:
When a body is displaced from its mean position and released, it starts vibrating.
Step 2: Detailed Explanation:
The ruler vibrates with its own natural frequency. However, because it is vibrating in air, it faces air resistance, and energy is lost in every cycle. This causes the amplitude to decrease over time.
Technically, these are damped vibrations. If we ignore air resistance for a short duration, they can be called natural or free vibrations.
Step 3: Final Answer: The vibrations produced are damped vibrations (or natural vibrations if damping is ignored).
(b)
Step 1: Understanding the Concept:
For a vibrating string or strip, the frequency is inversely proportional to the length of the vibrating part.
Step 2: Detailed Explanation:
When the ruler is pushed further onto the table, the length of the part projecting out (the vibrating length \(l\)) decreases.
Frequency \(f \propto \frac{1}{l}\).
Since the vibrating length is reduced, the frequency of vibration increases. This results in a shriller sound.
Step 3: Final Answer:
The frequency of vibration increases because the vibrating length of the ruler has decreased.