Sound

1. An electric bell is suspended inside an airtight glass bell-jar placed on the base of an air pump.
   2. When the electrical switch is pressed, the hammer strikes the gong, and the chime is heard distinctly.
   3. The vacuum pump is started to gradually evacuate the air from inside the jar.
   4. As the air density inside decreases, the sound of the bell becomes progressively fainter and fainter, until finally, when a high vacuum is achieved, NO SOUND is heard at all.
   5. However, through the transparent glass, the hammer can still be seen actively striking the gong.
   6. When air is allowed to rush back in, the sound is restored immediately.
   • Conclusion: Sound requires an elastic material medium and cannot travel through a vacuum.

Step 1: In echo sounding, the pulse travels to the seabed and back (total distance $= 2d$):

$$2d = v \times t$$

Step 2: Substitute $v = 1500\text{ m/s}$ and $t = 4\text{ s}$:

$$2d = 1500 \times 4 = 6000\text{ meters}$$

$$d = \frac{6000}{2} = \mathbf{3000\text{ meters} \quad (\text{or } 3\text{ km})}$$

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The depth of the sea is $3,000\text{ meters}$.

1. Governing Parameter: Pitch depends on Frequency ($f$); Loudness depends on Amplitude ($A$).
   2. Perception: Pitch determines whether a sound is shrill or grave/flat; Loudness determines whether a sound is loud or faint/soft.
   3. Mathematical Law: Pitch is independent of distance from the source; Loudness obeys the inverse-square law ($L \propto \frac{1}{r^2}$) and amplitude proportionality ($L \propto A^2$).

1. Speed: Sound travels vastly faster through solid steel ($\approx 5,000\text{ m/s}$) than through air ($\approx 340\text{ m/s}$). The acoustic vibration reaches the listener's ear through the steel rail roughly $15$ times faster!
   2. Energy Dissipation: Solids have tightly packed, highly elastic crystalline lattices that transmit acoustic vibrational energy over long distances with much less attenuation and scattering than the gaseous air.

• Audible Range: Between $20\text{ Hz}$ and $20,000\text{ Hz}$ ($20\text{ kHz}$).
• Frequencies below $20\text{ Hz}$ are called Infrasonic Sound (or infrasound).
• Frequencies above $20,000\text{ Hz}$ are called Ultrasonic Sound (or ultrasound).

• Bats utilize Echolocation.
• While flying, the bat emits continuous high-frequency ultrasonic squeaks (above $20,000\text{ Hz}$, up to $100\text{ kHz}$) from its mouth or nose.
• These ultrasonic waves strike surrounding obstacles or flying moths and reflect back as echoes.
• The bat's sensitive ears capture the reflected echo and its brain calculates the exact time delay and direction, mapping the obstacle's distance, size, and speed to navigate and hunt in total darkness.

• Timbre (Quality): The characteristic of a musical sound that enables a listener to distinguish between two sounds having the exact same pitch (frequency) and exact same loudness (amplitude).
• Reason for Difference: Even though both instruments play the identical fundamental frequency ($256\text{ Hz}$), the piano string and violin string vibrate with different harmonic overtones and distinct complex waveforms.
• The ear perceives this difference in resultant acoustic waveform as a distinctive musical timbre.