MP Board · Class 9 · Science · Sound(a) Explain how a vibrating body (such as a tuning fork) produces compressions and rarefactions in the surrounding air medium, propagating as a sound wave. (b) Explain the design and principle behind using soundboards and curved ceilings in large concert halls and auditoriums. (c) A flash of lightning is seen, and the sound of thunder is heard $4.5\text{ seconds}$ later. If the speed of sound in air is $344\text{ m/s}$, calculate the distance at which the lightning flash occurred. Why is the flash seen almost instantaneously?

(a) Production of Compressions and Rarefactions

\nWhen an object (like a prong of a tuning fork) vibrates, it transfers kinetic energy to the adjacent air particles:

• Formation of Compression (C): When the prong moves forward (outward), it pushes and compresses the air in front of it. This creates a region of high pressure and high density called a compression.
• Formation of Rarefaction (R): When the prong moves backward (inward), it leaves a region of low pressure and low density, causing the air particles to spread out. This region is called a rarefaction.
• As the object continues to vibrate rapidly back and forth, a series of compressions and rarefactions are produced in the air. These density/pressure variations propagate outward from the source, forming a longitudinal sound wave.

(b) Use of Curved Ceilings and Soundboards in Auditoriums

• Curved Ceilings: Auditoriums and concert halls are designed with curved ceilings so that sound reflecting from the ceiling reaches all corners of the hall uniformly after reflection.
• Soundboards: A soundboard is a curved concave board placed behind the stage.
  • Working Principle: The source of sound (speaker/performer) is placed at the focus of the curved board.
  • Sound waves striking the soundboard undergo multiple reflections and travel as parallel beams toward the audience, ensuring that the sound is evenly distributed and clearly audible throughout the hall.

(c) Numerical Solution

Given:

• Time delay between lightning and thunder ($t$) = $4.5\text{ s}$
• Speed of sound in air ($v$) = $344\text{ m/s}$

Formula: $$\text{Distance } (d) = \text{Speed } (v) \times \text{Time } (t)$$

Calculation: $$d = 344\text{ m/s} \times 4.5\text{ s}$$ $$d = 1548\text{ m} = 1.548\text{ km}$$

Reason for Instantaneous Vision:\nLight travels at an extremely high speed ($c \approx 3 \times 10^8\text{ m/s}$) compared to the speed of sound ($344\text{ m/s}$). Thus, light reaches our eyes almost instantly (in a fraction of a microsecond), while sound takes $4.5\text{ seconds}$ to travel the same distance.