(a) State three properties of waves (b)(i) Describe, with the aid of a labelled diagram, an experiment to show how the frequency of the note emitted by a vi...

(a) Three properties of waves are:

1. Reflection
2. Refraction
3. Diffraction

(b)(i) Experiment to show the relation between frequency and tension

A sonometer is set up as shown below. A uniform wire is stretched over two knife-edge bridges, A and B. One end of the wire passes over a smooth pulley and supports a scale pan. The distance AB is kept constant throughout the experiment.

1. Place a small paper rider at the middle of the wire between A and B.
2. Put a known total mass, including the scale pan, on the hanger. The tension in the wire is then \(T=mg\).
3. Strike a tuning fork of known frequency and hold its stem on the sonometer box. Pluck the wire gently.
4. Adjust the load until resonance occurs. At resonance the vibration of the wire is large and the paper rider is thrown off.
5. Record the total suspended mass and the frequency of the tuning fork.
6. Repeat the procedure with other tuning forks, keeping the vibrating length AB unchanged.

A set of readings is:

The graph of \(f\) against \(\sqrt{m}\) is:

The straight line passes through the origin. Its gradient is

\[\frac{512-256}{2.00-1.00}=256\ \text{Hz kg}^{-1/2}.\]

Hence \(f=256\sqrt{m}\). Since \(T=mg\), \(\sqrt{m}=\sqrt{T/g}\), and therefore

\[f\propto \sqrt{T}.\]

(b)(ii) Precautions

1. Keep the distance between the knife-edge bridges fixed, and ensure that the wire is taut and firmly held at the bridges.
2. Strike the tuning fork gently on a rubber pad and identify resonance only when the paper rider is thrown off, so that the frequency of the fork is not altered or damped.

(c) Virtual image formed by a concave mirror

When the object is between the pole \(P\) and principal focus \(F\), the reflected rays diverge. Their backward extensions meet behind the mirror at a virtual, erect and magnified image.