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Simple musical instruments

Chapter: Oscillations and Waves

Question 1 of 5 NDA MCQ

The time period of a 1 m long pendulum approximates to

Detailed Explanation

Correct Answer

✓ Option (c) is correct. The time period of a 1 m long pendulum approximates to 2 seconds.

📖 Governing Law / Core Concept

The time period \( T \) of a simple pendulum is governed by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where:
  • T = Time period (seconds)
  • L = Length of the pendulum (meters)
  • g = Acceleration due to gravity (approximately 9.81 m/s²)

🧪 Step-by-Step Breakdown

In this case, let \( L = 1 \) m. Substitute \( L \) into the time period formula:
\[ T = 2\pi \sqrt{\frac{1}{9.81}} \]
Calculate \( \sqrt{\frac{1}{9.81}} \):
\[ \sqrt{\frac{1}{9.81}} \approx 0.318 \]
Now, find \( T \):
\[ T \approx 2\pi \cdot 0.318 \approx 2.0 \text{ s} \]
Thus, the time period approximates to 2 seconds.

🔍 Option Analysis

- Option (a) 6 s: Too long for a 1 m pendulum. - Option (b) 4 s: Exceeds expected range for this length. - Option (d) 1 s: Too short, inconsistent with calculations.

⚡ Mnemonic / Speed-Run

For estimating pendulum time periods, use \( T \approx 2\sqrt{L} \) when \( g \) is considered as approximately 10 m/s² for quick mental calculations.

6. Visual Suggestion

6. Visual Suggestion

A diagram depicting a simple pendulum, showing the length \( L \), the pivot point, and the path of the bob swinging, aiding in visualizing the concept of the oscillation and its time period.

📖 Factual Verification & Reference

📖 Factual Verification & Reference:

Verified against NCERT Class XII Physics, Chapter 15 (Oscillations).

Question 2 of 5 NDA MCQ

We hear an echo due to

Detailed Explanation
✓

1. Correct Answer

Option B is correct. An echo occurs due to the reflection of sound waves.

📖 Core Concept

Echoes are a result of sound waves reflecting off surfaces back to the original source, producing repeated sound perceptions.

💡 3. Explanation

When sound waves are emitted, they travel and hit a surface, such as a wall or mountain. The waves reflect back, allowing the listener to hear the original sound after a delay. This phenomenon relies on:
Sound Reflection

❌ 4. Option Analysis

  • •Option A: Refraction involves bending of waves, not their reflection.
  • •Option C: Diffraction refers to the spreading of waves around obstacles, not reflection.
  • •Option D: Resonance amplifies sound but is unrelated to the phenomenon of echoing.
⚡

NDA Speed-Run / Mnemonic Shortcut

"Echoes reflect; they do not refract or distort!"

🎯

5. Key Takeaways

Echoes result from the reflection of sound waves from surfaces back to their origin.

Question 3 of 5 NDA MCQ

The frequency (f), wavelength (lambda) and speed(v) of a sound wave are related as

Detailed Explanation
✓

1. Correct Answer

Option D is correct. [The speed of sound is defined by the equation v = fλ.]

📖 Core Concept

The speed of sound in any medium is determined by its frequency and wavelength, expressed as v = fλ.

💡 3. Explanation

The relationship between frequency \( f \), wavelength \( \lambda \), and speed \( v \) is defined as:
v = fλ
Therefore, the speed of sound is directly proportional to its frequency and wavelength.

❌ 4. Option Analysis

  • •Option A: Incorrect, it asserts f = vλ, which reverses the relation.
  • •Option B: Incorrect as it states λ = vf, a misrepresentation of the relationship.
  • •Option C: Incorrect, it lacks a comprehensible physical connection.
⚡

NDA Speed-Run / Mnemonic Shortcut

Memorize v = fλ to quickly apply the relationship for sound waves.

🎯

5. Key Takeaways

The speed of sound is given by the relation v = fλ.

Question 4 of 5 NDA MCQ

The length of a simple pendulum is increased four times to its previous value while the mass is doubled. What is the ratio of the new and previous time period of the pendulum?

Detailed Explanation

💡 Solution

t:T 2:1

💡 Hints & Visual Guide

📌 Hints / Properties Used:

  • Time period of a simple pendulum is given as \( T = 2\pi \sqrt{\frac{l}{g}} \).
  • Mass of the bob does not affect the time period.

📊 Visual Diagram Suggestion:

[A labeled diagram of a simple pendulum indicating the length and its properties, including a side-by-side comparison of the time periods before and after the change in length and mass]

Question 5 of 5 NDA MCQ

The sound created in a big hall persists because of the repeated reflections. The phenomenon is called

Detailed Explanation

Correct Answer

✓ Option (a) is correct. The phenomenon is known as reverberation.

📖 Governing Law / Core Concept

Reverberation occurs due to the repeated reflection of sound waves in large spaces. The basic principle is formulated as: \[ \text{Sound Intensity} \propto \frac{1}{d^2} \] where \( d \) is the distance from the sound source.

🧪 Step-by-Step Breakdown

When sound waves encounter surfaces, they are reflected back multiple times before they dissipate. This results in the sound persisting in the environment. The reverberation time (\( T_r \)) can be calculated using Sabine's formula: \[ T_r = \frac{0.161 V}{A} \] where: - \( V \) = volume of the room (m³) - \( A \) = total surface area of absorption (m²) This reflection creates a layered effect of sound that can enhance auditory experiences, typical in concert halls.

🔍 Option Analysis

- **B: Dispersion** refers to the separation of waves into their component frequencies, not applicable here. - **C: Refraction** is the bending of waves as they pass through different media, irrelevant to sound persistence. - **D: Diffraction** is the bending of waves around obstacles; it contributes to sound behavior but not to persistent sound in a hall.

⚡ Mnemonic / Speed-Run

To remember reverberation, think "Room Echo" — R for Room, E for Echo.

6. Visual Suggestion

6. Visual Suggestion

A diagram illustrating sound wave propagation and reflection within a hall, showing how sound reflects off walls creating multiple sound paths leading to a persistent auditory experience.

📖 Factual Verification & Reference

📖 Factual Verification & Reference:

Verified against NCERT Class 11 Physics, Chapter 15 (Waves).

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