The Question is from NEET guide , and it was created by the author VENKATESWARARAO

Question

The wavelength of ultrasonic waves in air is of the order of

VENKATESWARARAO · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
	**Primary Concept**: Wavelength of a wave
	**Related Topics**: Frequency, Speed of Sound, Ultrasonic waves
	**Prerequisites**: Understanding the relationship between wavelength, frequency, and speed of a wave. Knowledge of the typical frequency range for ultrasonic waves.
## SOLUTION PATHWAY
**Given Information**:
	The question is about the order of magnitude of the wavelength of ultrasonic waves in air.
	We know that speed of sound in air is approximately 340 m/s
	Ultrasonic waves have frequencies above the human hearing range, typically above 20 kHz. We can assume a frequency of around $3.4 	imes 10^4 Hz$ for the calculation.
**Method & Steps**:
	1.  **Relate wavelength to speed and frequency**: The relationship between speed (v), frequency (f), and wavelength (λ) of a wave is given by: $v = fλ$ 
		Reasoning: We need to find the wavelength, and we know the speed of sound and the approximate frequency of ultrasonic waves.
		Formula/Rule: $λ = v/f$
	2.  **Calculate wavelength**:  
		Working:  $λ = \frac{340 \ m/s}{3.4 	imes 10^4 Hz} = 0.01 \ m = 1 \ cm$
		Key Point: The question asks for order of magnitude so an approximate frequency is fine.
	3.  **Compare with given options**: The calculated wavelength is 1 cm. The closest option is 0.5 cm.  
		Result:  The order of magnitude of the wavelength is $1 cm$ or $10^{-2}m$. So the wavelength is around $5 	imes {10^{ - 1}}cm$.
		Verification: We have calculated the wavelength based on an approximated frequency within the range of ultrasonic waves. 
 ## OPTION ANALYSIS
[A] ✓: This option is $5 	imes 10^{-1} cm = 0.5 cm$ which is the correct order of magnitude.
[B] :x: This option is too small. $5 	imes 10^{-3}cm$ is in the range of X-rays
[C] :x: This option is too large. $5 	imes 10^{1}cm$ is in the range of audible sound waves
[D] :x: This option is much too large. $5 	imes 10^{3}cm$ is in the range of radio waves.
 ## LEARNING AIDS
	**Common Mistakes**:
		1. **Using the wrong frequency**: Using a frequency outside the ultrasonic range will lead to an incorrect wavelength.
		2. **Incorrect unit conversion**: Not converting meters to centimeters can lead to an incorrect answer.
	**Quick Tips**:
		1. **Remember the speed of sound in air**: It's approximately 340 m/s.
		2. **Ultrasonic frequency range**: It's typically above 20 kHz.

VENKATESWARARAO · Answer

The correct Option is "$5 	imes {10^{ - 1}}cm$"

VENKATESWARARAO · Answer

$5 	imes {10^{ - 3}}cm$

VENKATESWARARAO · Answer

$5 	imes {10^1}cm$

VENKATESWARARAO · Answer

$5 	imes {10^3}cm$

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