MP Board · Class 9 · Science · Sound(a) Describe the structure and working mechanism of the human ear in detail with appropriate headings. (b) Numerical Problem: A sound wave has a frequency of $2\text{ kHz}$ and a wavelength of $35\text{ cm}$. Calculate the speed of the wave. How long will it take to travel a distance of $1.5\text{ km}$?

(a) Structure and Working Mechanism of the Human Ear

\nThe human ear is an extremely sensitive organ that enables us to hear. It converts pressure variations in air into electrical signals that travel to the brain via the auditory nerve. The ear is divided into three main parts:

1. Outer Ear:

   • Pinna: The outer part of the ear collects sound waves from the surroundings.
   • Auditory Canal: The collected sound passes through the ear canal to reach the eardrum.

2. Middle Ear:

   • Tympanic Membrane (Eardrum): A thin membrane located at the end of the auditory canal. When compressions of a sound wave reach it, the pressure increases and pushes the eardrum inward. When rarefactions reach it, the eardrum moves outward, causing it to vibrate.
   • Auditory Ossicles (Malleus, Incus, Stapes): Three tiny bones—hammer, anvil, and stirrup—amplify the vibrations received from the eardrum several times.

3. Inner Ear:

   • Cochlea: The middle ear transmits these amplified pressure variations to the cochlea in the inner ear. The cochlea converts these mechanical sound vibrations into electrical signals.
   • Auditory Nerve: These electrical signals are sent to the brain via the auditory nerve, where the brain interprets them as sound.

(b) Solution to Numerical Problem

Given Data:

• Frequency ($f$) = $2\text{ kHz} = 2000\text{ Hz}$
• Wavelength ($\lambda$) = $35\text{ cm} = \frac{35}{100}\text{ m} = 0.35\text{ m}$
• Distance ($d$) = $1.5\text{ km} = 1.5 \times 1000\text{ m} = 1500\text{ m}$

Step 1: Calculate the speed of the sound wave ($v$) $$\text{Speed } (v) = \text{Frequency } (f) \times \text{Wavelength } (\lambda)$$ $$v = 2000\text{ Hz} \times 0.35\text{ m} = 700\text{ m/s}$$

Step 2: Calculate the time taken ($t$) to travel $1.5\text{ km}$ $$\text{Time } (t) = \frac{\text{Distance } (d)}{\text{Speed } (v)}$$ $$t = \frac{1500\text{ m}}{700\text{ m/s}} = \frac{15}{7}\text{ s} \approx 2.14\text{ seconds}$$

Answer:

• The speed of the sound wave is $700\text{ m/s}$.
• The time taken to travel $1.5\text{ km}$ is $2.14\text{ seconds}$.