The Question is from neet-physics waves velocity-of-sound, and it was created by the author P.NARASIMHA

Question

A sound wave travels through air with a frequency of 500 Hz. If the air temperature increases, keeping other factors constant, the velocity of the sound wave will:

P.NARASIMHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
 **Primary Concept**: Speed of sound in air
 **Related Topics**: Temperature dependence of sound speed, kinetic theory of gases
 **Prerequisites**: Understanding of wave properties, relationship between temperature and molecular kinetic energy.
## SOLUTION PATHWAY
**Given Information**:
  Frequency of sound wave = 500 Hz
  Air temperature increases (other factors constant)
**Method & Steps**:
 1. Understand the relationship between the speed of sound and temperature.
  Reasoning: The speed of sound in air is directly proportional to the square root of the absolute temperature.  Higher temperatures mean higher molecular kinetic energy, leading to faster propagation of sound waves.
  Formula/Rule: $v = 331.4 + 0.6T$, where $v$ is the speed of sound in m/s and $T$ is the temperature in Celsius.  Alternatively, a more precise formula involves the adiabatic index and gas constant.
 2. Analyze the effect of temperature increase.
  Working: Since the temperature increases, and the speed of sound is directly related to the square root of the absolute temperature, the speed of sound will increase.
  Key Point: The frequency remains constant because the source of the sound wave isn't changing.
 3. State the final conclusion.
  Result: The velocity of the sound wave will increase.
  Verification: Using the formula above, if T increases, v increases.
 ## OPTION ANALYSIS
A ✓: Increase: Correct. The speed of sound increases with increasing temperature.
B :x: Decrease: Incorrect.  The speed of sound does not decrease with increasing temperature.
C :x: Remain the same: Incorrect. The speed of sound is temperature-dependent.
D :x: Become zero: Incorrect. The speed of sound will not become zero unless the medium is completely absent.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing the relationship between speed, frequency, and wavelength: Remember that $v = fλ$, where $v$ is speed, $f$ is frequency, and $λ$ is wavelength. A change in temperature affects the speed, not necessarily the frequency directly.
  2.Ignoring the absolute temperature:  You must use the absolute temperature (Kelvin) in precise calculations of sound speed.
 **Quick Tips**:
  1.Remember the general trend: higher temperature implies higher speed of sound in air.
  2.Visualize the increased molecular motion at higher temperatures leading to faster sound wave propagation.

P.NARASIMHA · Answer

The correct Option is "Increase"

P.NARASIMHA · Answer

Decrease

P.NARASIMHA · Answer

Remain the same

P.NARASIMHA · Answer

Become zero

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