(a)(i) What is meant by resonance? (ii) Outline the necessary steps taken in a simple experiment to illustrate top resonance (iii) Explain why a vibrating t...

(a)(i) Resonance occurs when a body is made to vibrate at its own natural frequency by a periodic force having the same frequency; the amplitude of vibration then becomes a maximum.

(ii) Experiment to illustrate resonance (resonance tube):

• Hold a vibrating tuning fork of known frequency just above the open end of a tube whose air-column length can be varied (e.g. a tube dipping in water, raised or lowered).
• Slowly change the length of the air column.
• At a particular length the sound suddenly becomes very loud; here the natural frequency of the air column equals the frequency of the fork, i.e. resonance occurs.
• Measure that resonating length.

(iii) When the stem of the vibrating fork is pressed on a table top, it forces the large table surface to vibrate at the same frequency (forced vibration / resonance). The large surface sets a much greater volume of air in motion than the thin prongs alone, so more sound energy reaches the ear and the note sounds louder. In air, only the small prongs move the air, so the sound is faint.

(b) Concave-mirror uses.

(i) To ignite carbon paper: the mirror faces the sun, whose rays are parallel to the axis; the mirror converges them to its principal focus \(F\). The paper placed at \(F\) receives concentrated heat and burns.

(ii) To produce an exact copy (same size) of a picture on a screen: place the object at the centre of curvature \(C\) (i.e. at \(2f\)). The mirror then forms a real, inverted image, of exactly the same size, also at \(C\), which can be received on a screen.