Waves

Step 1: Determine the possible initial frequencies of the unknown fork. Let the unknown frequency be . The reference frequency is Hz. The beat frequency is Hz. This gives two possibilities for : - Hz - Hz
Step 2: Analyze the effect of adding wax. Adding wax to a tuning fork increases its mass, which causes its frequency to decrease. Let the new frequency of the first fork be , where .
Step 3: Test the two possibilities with the new information. The new beat frequency is 3 Hz. - Case A: Assume initial Hz. When wax is added, its frequency will be slightly less than 260 Hz. The new beat frequency is . As moves from 260 towards 256, the difference decreases. It is possible for the beat frequency to become 3 Hz. This is consistent. - Case B: Assume initial Hz. When wax is added, its frequency will be slightly less than 252 Hz. The new beat frequency is . As decreases from 252, it moves further away from 256, so the difference will increase. The beat frequency would become greater than 4 Hz, not 3 Hz. This contradicts the observation.
Step 4: Conclude the initial frequency. Only the first case is consistent with the experimental result. Therefore, the original frequency of the first fork was 260 Hz.

Step 1: Recall the relationship between intensity and distance for an isotropic source. For a source radiating uniformly in all directions, the intensity decreases with the square of the distance from the source. This is the inverse square law: This means that the product is constant. Therefore, we can write .
Step 2: Identify the given values. - Initial intensity W/m . - Initial distance m. - Final distance m. - We need to find the final intensity .
Step 3: Solve for .