Sound

Sound:
Sound is a form of energy that produces the sensation of hearing in our ears. It is a mechanical wave that requires a material medium (solid, liquid, or gas) for its propagation.

How sound is produced:
Sound is produced by the vibration of objects. When an object vibrates, it causes the particles of the surrounding medium to vibrate. These vibrations travel through the medium in the form of a wave, which we perceive as sound.

Example: When we pluck a stretched rubber band, it vibrates and produces sound. When a drum is beaten, its membrane vibrates and produces sound. The vibrating object acts as the source of sound.

Production of Compressions and Rarefactions:

Consider a vibrating tuning fork as the source of sound.

- When the prong of the tuning fork moves outward (forward), it pushes the air particles in front of it. These particles get crowded together, forming a region of high pressure called compression (C).
- When the prong moves inward (backward), it creates a region where air particles are spread apart, forming a region of low pressure called rarefaction (R).
- As the tuning fork continues to vibrate, a series of compressions and rarefactions are produced alternately in the air.

Diagram (description):
$$\text{Source} \rightarrow \underbrace{||||}_{C} \quad \underbrace{\quad\quad}_{R} \quad \underbrace{||||}_{C} \quad \underbrace{\quad\quad}_{R} \quad \underbrace{||||}_{C} \rightarrow$$

Where $C$ = Compression (region of high pressure, particles close together) and $R$ = Rarefaction (region of low pressure, particles spread apart).

These compressions and rarefactions propagate through the air as a longitudinal sound wave.

Sound wave is called a longitudinal wave because the particles of the medium vibrate in the same direction as the direction of propagation of the wave.

Explanation:
When a sound wave travels through air, the air particles are displaced back and forth along the direction in which the wave is moving. This creates alternating regions of compressions (high pressure) and rarefactions (low pressure) along the direction of wave propagation.

Since the direction of particle vibration is parallel (along the same line) to the direction of wave propagation, sound waves are classified as longitudinal waves.

This is in contrast to transverse waves (like light waves), where particle vibration is perpendicular to the direction of wave propagation.

The characteristic of sound that helps us identify a friend by his voice in a dark room is quality (or timbre) of sound.

Explanation:
Even if two sounds have the same pitch (frequency) and the same loudness (amplitude), they can differ in quality. Quality of sound depends on the waveform of the sound, which is determined by the number and relative intensities of the overtones (harmonics) present in the sound.

Every person has a unique vocal structure, so the sound produced by each person has a unique waveform (quality/timbre). This unique quality allows us to distinguish one person's voice from another even in darkness.

Given/Known:
- Flash (light) and thunder (sound) are produced simultaneously during lightning.
- Speed of light $= 3 \times 10^8 \ \text{m s}^{-1}$
- Speed of sound in air $\approx 344 \ \text{m s}^{-1}$

Reason:
The speed of light is enormously greater than the speed of sound. Light travels at $3 \times 10^8 \ \text{m s}^{-1}$, while sound travels at only about $344 \ \text{m s}^{-1}$ in air.

Therefore, light from the flash reaches our eyes almost instantaneously, while sound (thunder) takes a much longer time to travel the same distance. This is why we see the flash first and hear the thunder a few seconds later.

Conclusion: The time gap between seeing the flash and hearing the thunder is due to the vast difference in the speeds of light and sound.

Given:
- Speed of sound in air, $v = 344 \ \text{m s}^{-1}$
- Frequency $f_1 = 20 \ \text{Hz}$
- Frequency $f_2 = 20 \ \text{kHz} = 20{,}000 \ \text{Hz}$

Formula:
$$\lambda = \frac{v}{f}$$

**For $f_1 = 20 \ \text{Hz}$:**
$$\lambda_1 = \frac{344}{20} = 17.2 \ \text{m}$$

**For $f_2 = 20{,}000 \ \text{Hz}$:**
$$\lambda_2 = \frac{344}{20{,}000} = 0.0172 \ \text{m} = 1.72 \ \text{cm}$$

Result:
- Wavelength corresponding to 20 Hz $= 17.2 \ \text{m}$
- Wavelength corresponding to 20 kHz $= 0.0172 \ \text{m}$ (or $1.72 \ \text{cm}$)

Given:
- Speed of sound in air, $v_{\text{air}} = 346 \ \text{m s}^{-1}$ (standard value used in NCERT)
- Speed of sound in aluminium, $v_{\text{Al}} = 6420 \ \text{m s}^{-1}$ (standard value from NCERT table)
- Let the length of the aluminium rod $= d$

Formula:
$$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$

Time taken by sound through air:
$$t_{\text{air}} = \frac{d}{v_{\text{air}}} = \frac{d}{346}$$

Time taken by sound through aluminium:
$$t_{\text{Al}} = \frac{d}{v_{\text{Al}}} = \frac{d}{6420}$$

Ratio:
$$\frac{t_{\text{air}}}{t_{\text{Al}}} = \frac{d/346}{d/6420} = \frac{6420}{346} \approx 18.55 \approx 18.5$$

$$\boxed{\frac{t_{\text{air}}}{t_{\text{Al}}} \approx 18.5 : 1}$$

This means sound takes about 18.5 times longer to travel through air than through aluminium for the same distance.

Given:
- Frequency of sound, $f = 100 \ \text{Hz}$
- Time $= 1 \ \text{minute} = 60 \ \text{seconds}$

Concept:
Frequency is defined as the number of vibrations (oscillations) per second.
$$f = \frac{\text{Number of vibrations}}{\text{Time (in seconds)}}$$

Calculation:
$$\text{Number of vibrations in 1 minute} = f \times t = 100 \ \text{Hz} \times 60 \ \text{s}$$
$$= 6000 \ \text{vibrations}$$

Answer: The source vibrates 6000 times in one minute.

Yes, sound follows the same laws of reflection as light does.

Laws of Reflection of Sound:

1. First Law: The angle of incidence of the sound wave is equal to the angle of reflection.
$$\angle i = \angle r$$

2. Second Law: The incident sound wave, the reflected sound wave, and the normal to the reflecting surface at the point of incidence — all lie in the same plane.

Explanation:
Just like light, when sound waves strike a hard surface (like a wall, cliff, or building), they bounce back. The direction of the reflected sound wave obeys the same geometrical rules as reflected light. This is why we hear echoes — the reflected sound follows the same laws as reflected light.

Practical evidence: The phenomenon of echo and the working of a megaphone, stethoscope, and soundboards all demonstrate that sound obeys the laws of reflection.