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Physics - Sound (Echoes, Vibrations, Resonance)

Grade 10ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Sound waves are longitudinal mechanical waves that require a material medium for propagation. In the ICSE Grade 10 syllabus, the focus is on the reflection of sound and the nature of vibrations.

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An Echo is the sound heard after reflection from a rigid obstacle (such as a cliff or a wall). To hear a distinct echo, the reflected sound must reach the ear at least 0.1 s0.1 \text{ s} after the original sound, as the persistence of hearing for the human ear is 0.1 s0.1 \text{ s}.

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The minimum distance required to hear an echo in air is approximately 17.2 m17.2 \text{ m}. This is calculated using d=v×t2d = \frac{v \times t}{2} where v≈344 m/sv \approx 344 \text{ m/s} and t=0.1 st = 0.1 \text{ s}.

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Free Vibrations occur when a body vibrates with its natural frequency in the absence of any external or resistive forces. The amplitude remains constant over time.

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Damped Vibrations occur when the amplitude of vibrations decreases over time due to resistive forces (like air friction). The frequency is slightly lower than the natural frequency, and energy is dissipated to the surroundings.

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Forced Vibrations are vibrations produced in a body by an external periodic force. The body vibrates with the frequency of the external force rather than its own natural frequency.

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Resonance is a special case of forced vibrations. When the frequency of the external periodic force is exactly equal to the natural frequency of the body, the body vibrates with a significantly increased amplitude.

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The Quality (Timbre) of a sound allows us to distinguish between two sounds of the same pitch and loudness. it depends on the waveform and the presence of overtones/subsidiary notes.

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Loudness is a subjective quantity related to the intensity of sound. It depends on the amplitude (L∝A2L \propto A^2), the surface area of the vibrating body, and the distance from the source.

📐Formulae

d=v×t2d = \frac{v \times t}{2}

v=fλv = f \lambda

f=1Tf = \frac{1}{T}

I∝A2I \propto A^2

f = \frac{1}{2l} \sqrt{ rac{T}{m}} \text{ (For a stretched string)}

💡Examples

Problem 1:

A RADAR sends a signal to an aeroplane at a distance dd and receives the echoed signal after 4×10−5 s4 \times 10^{-5} \text{ s}. If the speed of the signal is 3×108 m/s3 \times 10^8 \text{ m/s}, calculate the distance dd.

Solution:

Given t=4×10−5 st = 4 \times 10^{-5} \text{ s} and v=3×108 m/sv = 3 \times 10^8 \text{ m/s}. Using the echo formula: d=v×t2d = \frac{v \times t}{2} d=(3×108)×(4×10−5)2d = \frac{(3 \times 10^8) \times (4 \times 10^{-5})}{2} d=12×1032=6000 m=6 kmd = \frac{12 \times 10^3}{2} = 6000 \text{ m} = 6 \text{ km}

Explanation:

The signal travels to the object and back, covering a total distance of 2d2d. Dividing the total distance by 2 gives the one-way distance to the aeroplane.

Problem 2:

Two tuning forks AA and BB of frequencies 256 Hz256 \text{ Hz} and 512 Hz512 \text{ Hz} are vibrated. Which one will produce a sound with a higher pitch? If both have the same amplitude, which one is louder?

Solution:

  1. Tuning fork BB will have a higher pitch because pitch is directly proportional to frequency (512 Hz>256 Hz512 \text{ Hz} > 256 \text{ Hz}). 2. Both will have the same loudness because loudness depends on the amplitude, which is given as equal for both.

Explanation:

Pitch is a characteristic of sound determined by frequency. Loudness is a characteristic determined primarily by the amplitude of the vibration.

Problem 3:

A tuning fork is struck and held over the mouth of a hollow tube submerged in water. As the length of the air column is adjusted, a loud sound is heard at a specific point. Identify the phenomenon.

Solution:

The phenomenon is Resonance.

Explanation:

When the natural frequency of the air column in the tube matches the frequency of the vibrating tuning fork, forced vibrations with maximum amplitude occur, resulting in a loud sound.