1.0 Production and Propagation of Sound
Sound is a form of energy that produces the sensation of hearing in our ears. In Physics, sound is produced by vibrations—the rapid to-and-fro motion of an object about its mean position. Without vibration, there is no sound.
Sound as a Mechanical Wave
Sound requires a material medium (solid, liquid, or gas) to travel. It cannot travel through a vacuum because there are no particles to vibrate and carry the energy.
- Medium Density: Speed of sound is highest in Solids and lowest in Gases.
- Nature of Wave: Sound travels as a Longitudinal Wave, consisting of Compressions and Rarefactions.
1.1 Characteristics of Sound Waves
To describe a sound wave, we use specific technical terms that determine how we perceive the sound:
The Wave Equation
$$V = f \times \lambda$$
Where: $V$ = Speed of sound, $f$ = Frequency (Hz), $\lambda$ (Lambda) = Wavelength (m).
- Amplitude (A): The maximum displacement of a particle from its mean position. It determines the Loudness.
- Frequency (f): Number of vibrations per second. Measured in Hertz (Hz). It determines the Pitch.
- Time Period (T): Time taken for one complete vibration. ($T = 1/f$)
This classic experiment proves sound needs a medium. As air is pumped out of a jar containing a ringing electric bell, the sound becomes fainter and eventually disappears, even though the hammer is still seen striking the gong.
A tuning fork produces 256 vibrations in 2 seconds. Find its frequency and time period.
Solution:
1. Frequency ($f$): Total Vibrations / Total Time = $256 / 2 = 128\,Hz$.
2. Time Period ($T$): $1 / f = 1 / 128 \approx 0.0078\,seconds$.
Final Answer: Frequency is $128\,Hz$ and Time Period is $0.0078\,s$.
Sound travels through steel at about $5,960\,m/s$, which is nearly 17 times faster than its speed in air! This is why you can hear a train coming from a distance by putting your ear to the rail.
2.0 Subjective Characteristics of Sound
Two sounds can be different even if they travel through the same medium. We distinguish between them using three main characteristics: Loudness, Pitch, and Quality (Timbre).
2.1 Loudness and Intensity
Loudness is the characteristic that allows us to distinguish a faint sound from a loud sound. It depends primarily on the Amplitude of the vibration.
- Relationship: Loudness is directly proportional to the square of the amplitude ($L \propto A^2$).
- Unit: Measured in Decibels (dB).
- Factors: Depends on amplitude, distance from the source, and the surface area of the vibrating body.
2.2 Pitch and Frequency
Pitch is the characteristic that distinguishes a "shrill" sound from a "flat" or "grave" sound. It depends entirely on the Frequency of vibration.
- High Pitch: High frequency (e.g., a woman's voice, a whistling bird).
- Low Pitch: Low frequency (e.g., a man's voice, the roar of a lion).
2.3 Quality or Timbre
Quality is the characteristic that allows us to distinguish between sounds produced by different sources (like a piano and a violin) even if they have the same loudness and pitch. It depends on the waveform and the presence of overtones.
The Audible Range
Human Hearing Range: $20\,Hz$ to $20,000\,Hz$
Sounds below $20\,Hz$ are Infrasonic; sounds above $20,000\,Hz$ are Ultrasonic.
Remember: If you strike a drum harder, you increase the amplitude (making it louder). If you tighten the skin of the drum, you increase the frequency (making it higher pitched). They are independent of each other!
If the amplitude of a vibrating body is tripled, by how many times will its loudness increase?
Solution:
1. We know that Loudness $\propto (Amplitude)^2$.
2. Let original amplitude be $A_1$ and new amplitude be $A_2 = 3A_1$.
3. New Loudness $\propto (3A_1)^2 = 9A_1^2$.
Final Answer: The loudness will increase by 9 times.
Bats navigate using Ultrasound. They emit high-frequency squeaks beyond $20,000\,Hz$ and listen for the echoes to detect obstacles and prey. This process is called Echolocation.
3.0 Reflection of Sound and Echoes
Just like light, sound waves bounce back when they strike a hard surface. This phenomenon is called the Reflection of Sound. It follows the same laws as light: the angle of incidence is equal to the angle of reflection.
3.1 What is an Echo?
An Echo is the repetition of sound heard after it is reflected from a distant hard surface (like a cliff, a wall, or a mountain). To hear a distinct echo, our ears must be able to distinguish the original sound from the reflected one.
Conditions for an Echo
- Persistence of Hearing: The human ear can distinguish two sounds only if there is a time gap of at least 0.1 seconds between them.
- Minimum Distance: Taking the speed of sound as $340\,m/s$, the sound must travel $340 \times 0.1 = 34\,m$ (total go-and-return distance). Therefore, the minimum distance of the obstacle must be 17 metres.
- The reflecting surface must be large enough and hard.
The Echo Formula
$$d = \frac{V \times t}{2}$$
Where: $d$ = distance to the obstacle, $V$ = speed of sound, $t$ = total time taken.
3.2 SONAR and its Uses
SONAR stands for Sound Navigation and Ranging. It uses Ultrasonic waves to measure the depth of the ocean or to detect underwater objects like submarines or shoals of fish. The principle is based on Echo Ranging.
While an echo is a single reflection, Reverberation is the persistence of sound due to multiple reflections in a closed hall. This causes the sound to become muffled and unclear. To prevent this, cinema halls use sound-absorbing materials like thermocol or heavy curtains.
A SONAR device on a ship sends a signal and receives an echo 4 seconds later from the sea bed. If the speed of sound in water is 1500 m/s, find the depth of the sea.
Solution:
1. Speed ($V$): $1500\,m/s$
2. Time ($t$): $4\,s$
3. Formula: $Depth\,(d) = (V \times t) / 2$
4. Calculation: $d = (1500 \times 4) / 2 = 6000 / 2 = 3000\,m$.
Final Answer: The depth of the sea is $3000$ metres (or 3 km).
The Stethoscope used by doctors works on the principle of multiple reflection of sound. The sound of your heartbeat is guided through the tube by reflecting multiple times off the inner walls until it reaches the doctor's ears.
4.0 Types of Vibrations
In Physics, not all vibrations are the same. Depending on whether an external force is applied or if the medium resists the motion, we classify vibrations into three main types: Free, Forced, and Damped vibrations, along with the special case of Resonance.
4.1 Free and Damped Vibrations
- Free (Natural) Vibrations: Vibrations of a body with its own natural frequency in the absence of any external force or friction. The amplitude remains constant.
- Damped Vibrations: In the real world, friction and air resistance cause the amplitude of vibrations to decrease over time until the body stops. This is called damping.
4.2 Forced Vibrations
When a body is made to vibrate by an external periodic force, it vibrates with the frequency of the applied force rather than its own natural frequency. These are called forced vibrations.
Example: When the stem of a vibrating tuning fork is pressed against a table top, the table is forced to vibrate.
4.3 Resonance: A Special Case
Resonance is a special type of forced vibration. It occurs when the frequency of the external force becomes exactly equal to the natural frequency of the body.
The Condition for Resonance
$$f_{external} = f_{natural}$$
Result: The body vibrates with a maximum amplitude, producing a loud sound.
Marching soldiers are ordered to break their step (walk normally) while crossing a suspension bridge. If the frequency of their rhythmic marching steps matches the natural frequency of the bridge, resonance could occur, causing the bridge to vibrate with such large amplitude that it might collapse!
Why does an empty glass tumbler sometimes crack when a very loud, high-pitched note is sung near it?
Solution:
1. Every glass tumbler has a natural frequency of vibration.
2. When a note is sung at that exact frequency, Resonance occurs.
3. The glass starts vibrating with a very large amplitude.
4. Since glass is brittle, it cannot withstand the mechanical stress of such high-amplitude vibrations and shatters.
When you "tune" a radio to a specific station, you are actually adjusting the electrical frequency of your radio circuit to match the frequency of the station's broadcast. This is an example of Electrical Resonance!