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The wavelength of ultrasonic waves in air is of the order of
- a)5 x 10 − 5 cm
- b)5 x 10 − 8 cm
- c)5 x 105 cm
- d)5 x 108 cm
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The wavelength of ultrasonic waves in air is of the order ofa)5 x 10 &...
Explanation:
Ultrasonic waves in air:
- Ultrasonic waves are sound waves with frequencies higher than the upper audible limit of human hearing.
- In air, ultrasonic waves have wavelengths that are very short due to their high frequency.
Wavelength calculation:
- The speed of sound in air at room temperature is approximately 343 m/s.
- The formula to calculate wavelength is: Wavelength = Speed of sound / Frequency
- Let's assume a typical ultrasonic frequency of 20 kHz (20,000 Hz).
Wavelength calculation:
- Wavelength = 343 m/s / 20,000 Hz
- Wavelength = 0.01715 m
- Converting to cm: 0.01715 m * 100 = 1.715 cm
Order of magnitude:
- The order of magnitude is the power of 10 when a number is expressed in scientific notation.
- The order of magnitude of 1.715 cm is 10^-2, which is closest to 10^-5.
Therefore, the correct answer is option A) 5 x 10^-5 cm as it represents the order of magnitude of the wavelength of ultrasonic waves in air.
Ultrasonic waves in air:
- Ultrasonic waves are sound waves with frequencies higher than the upper audible limit of human hearing.
- In air, ultrasonic waves have wavelengths that are very short due to their high frequency.
Wavelength calculation:
- The speed of sound in air at room temperature is approximately 343 m/s.
- The formula to calculate wavelength is: Wavelength = Speed of sound / Frequency
- Let's assume a typical ultrasonic frequency of 20 kHz (20,000 Hz).
Wavelength calculation:
- Wavelength = 343 m/s / 20,000 Hz
- Wavelength = 0.01715 m
- Converting to cm: 0.01715 m * 100 = 1.715 cm
Order of magnitude:
- The order of magnitude is the power of 10 when a number is expressed in scientific notation.
- The order of magnitude of 1.715 cm is 10^-2, which is closest to 10^-5.
Therefore, the correct answer is option A) 5 x 10^-5 cm as it represents the order of magnitude of the wavelength of ultrasonic waves in air.
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Community Answer
The wavelength of ultrasonic waves in air is of the order ofa)5 x 10 &...
Ultrasonic waves are sound waves with frequencies higher than the audible range (generally above 20 kHz). The wavelength of ultrasonic waves in air can be calculated using the formula:
λ = v / f
λ = v / f
Where:
λ is the wavelength,
v is the velocity of sound in air (approximately 343 m/s at room temperature),
f is the frequency.
λ is the wavelength,
v is the velocity of sound in air (approximately 343 m/s at room temperature),
f is the frequency.
For ultrasonic waves, if we take a typical frequency of 1 MHz (1 x 10⁶ Hz), the wavelength would be:
λ = (343 m/s) / (1 x 10⁶ Hz) = 3.43 x 10⁻⁴ m or 3.43 x 10⁻² cm.
λ = (343 m/s) / (1 x 10⁶ Hz) = 3.43 x 10⁻⁴ m or 3.43 x 10⁻² cm.
Thus, the wavelength of ultrasonic waves in air is generally in the range of 5 x 10⁻⁵ cm.
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