Question

The longest wavelength of the ultrasonic waves in air at room temperature is nearly:
1. 11 mm
2. 21 mm
3. 17 mm
4. 27 mm

Answer 1

Correct Answer - Option 3 : 17 mm

Concept:

Wavelength (λ) is equal to the distance traveled by the wave during the time in which any one particle of the medium completes one vibration about its mean position. It is the length of one wave.

Frequency (f) of vibration of a particle is defined as the number of vibrations completed by the particle in one second. It is the number of complete wavelengths traversed by the wave in one second.

The relation between velocity(v), frequency(f), and wavelength(λ): v = f × λ

Calculation:

The frequency of ultrasonic is around f = 2 × 10⁴ Hz

Velocity of sound is(v) = 330 m/sec

\(λ=\frac{v}{f}=\frac{330}{2×{10}^4 }\)

λ = 1.65 × 10^-2 m

λ ≈ 17 mm