MP Board · Class 9 · Science · Sound(a) Why is sound classified as a mechanical wave? Describe an experiment using a bell jar to demonstrate that sound requires a material medium to propagate and cannot travel through a vacuum. (b) Explain why sound travels faster in solids than in gases. (c) A sound source generates a wave with a frequency of $600\text{ Hz}$ and a speed of $300\text{ m/s}$ in Medium A. Calculate its wavelength in Medium A. If this sound wave passes into Medium B where its speed becomes $1200\text{ m/s}$, calculate its new wavelength in Medium B.

(a) Mechanical Nature of Sound and Bell Jar Experiment

Why Sound is a Mechanical Wave:\nSound is called a mechanical wave because it requires a physical material medium (such as solid, liquid, or gas) to propagate. It travels through the periodic vibration of medium particles that transfer energy from one point to another without the net movement of the particles themselves.

Electric Bell Jar Experiment:

• Setup: An electric bell is suspended inside an airtight glass bell jar connected to a vacuum pump.
• Procedure:
  1. Initially, air is present inside the bell jar. When the switch is pressed, the electric bell rings, and the sound is heard clearly outside.
  2. Now, start the vacuum pump to gradually remove air from inside the jar.
• Observation: As the air inside the jar is pumped out, the sound of the bell becomes progressively fainter, even though the hammer continues to strike the gong visually. When almost all the air is removed (vacuum is created), no sound can be heard.
• Conclusion: Sound cannot travel through a vacuum; it strictly requires a material medium to propagate.

(b) Speed of Sound in Solids vs Gases

\nSound travels significantly faster in solids than in gases due to two main reasons:

1. Particle Density and Proximity: Particles in solids are closely packed together, whereas in gases they are far apart. Vibrations are passed on much more rapidly from particle to particle in solids.
2. Elasticity of Medium: Solids have higher elasticity (resistance to deformation and ability to spring back quickly) compared to gases. Higher elasticity allows sound waves to travel much faster.

(c) Numerical Problem

Given:

• Frequency of sound wave ($f$) = $600\text{ Hz}$ (constant across media)
• Speed in Medium A ($v_A$) = $300\text{ m/s}$
• Speed in Medium B ($v_B$) = $1200\text{ m/s}$

Step 1: Calculate Wavelength in Medium A ($\lambda_A$)\nFormula relating speed, frequency, and wavelength:

$$\nv = f \times \lambda \implies \lambda = \frac{v}{f} $$ $$ \lambda_A = \frac{v_A}{f} = \frac{300\text{ m/s}}{600\text{ Hz}} = 0.5\text{ m} $$

Step 2: Calculate Wavelength in Medium B ($\lambda_B$)\nWhen sound passes from one medium to another, its frequency ($f$) remains unchanged, but speed and wavelength change.

$$ \lambda_B = \frac{v_B}{f} = \frac{1200\text{ m/s}}{600\text{ Hz}} = 2.0\text{ m} $$

• Wavelength in Medium A: $0.5\text{ m}$
• Wavelength in Medium B: $2.0\text{ m}$