Ultrasonic, Infrasonic and Audible waves travel through a medium with speeds `v_(u), v_(l), v_(a)` respectively, then

Options

A. `v_(u), v_(i), v_(a)` are nearly equal
B. `v_(u) ge v_(a) ge v_(i)`
C. `v_(u) ge v_(a) ge v_(i)`
D. `v_(a) ge v_(u) and v_(u) ~~ v_(i`

Answer

To solve the question regarding the speeds of ultrasonic, infrasonic, and audible waves, we will analyze the relationship between these speeds based on the properties of sound waves in a medium.

### Step-by-Step Solution:

1. **Understanding Wave Types**:
- **Ultrasonic Waves**: These are sound waves with frequencies above the audible range (greater than 20 kHz).
- **Infrasonic Waves**: These are sound waves with frequencies below the audible range (less than 20 Hz).
- **Audible Waves**: These are sound waves within the frequency range that humans can hear (approximately 20 Hz to 20 kHz).

2. **Speed of Sound Formula**:
- The speed of sound in a medium is given by the formula:
\[ v = \sqrt{\frac{k}{\rho}} \]
where:
- \( v \) is the speed of sound,
- \( k \) is the bulk modulus of the medium (a measure of the medium's resistance to compression),
- \( \rho \) is the density of the medium.

3. **Dependency on Medium Properties**:
- The speed of sound is determined by the properties of the medium (bulk modulus and density) and does not depend on the frequency or wavelength of the sound waves.
- This means that regardless of whether the waves are ultrasonic, infrasonic, or audible, their speeds depend solely on the characteristics of the medium through which they are traveling.

4. **Conclusion**:
- Since the speed of sound does not depend on the type of wave (ultrasonic, infrasonic, or audible), we can conclude that:
\[ v_u \approx v_l \approx v_a \]
- Thus, the speeds of ultrasonic, infrasonic, and audible waves in the same medium are nearly equal.

5. **Final Answer**:
- The correct option is that the speeds of ultrasonic, infrasonic, and audible waves are nearly equal.