Question

What is the relation between sound velocity ($ V $), frequency ($ \gamma $), and wavelength ($ \lambda $)?

• A. $ V = \gamma \lambda $
• B. $ \gamma = \frac{V}{\lambda} $
• C. $ \lambda = \frac{V}{\gamma} $
• D. All of these

Hint:

The relationship between velocity, frequency, and wavelength is fundamental in wave mechanics. Always remember the basic wave equation $ V = \gamma \lambda $ and its rearrangements $ \gamma = \frac{V}{\lambda} $ and $ \lambda = \frac{V}{\gamma} $. These equations apply to all types of waves, including sound waves.

Answer 1

The Correct Option is D

Step 1: Recall the Relationship Between Velocity, Frequency, and Wavelength.
The relationship between the velocity ($ V $), frequency ($ \gamma $), and wavelength ($ \lambda $) of a wave is given by: \[ V = \gamma \lambda. \] This equation can be rearranged to express frequency or wavelength in terms of the other variables: \[ \gamma = \frac{V}{\lambda}, \quad \lambda = \frac{V}{\gamma}. \] Step 2: Analyze Each Option.
Option (1): \( V = \gamma \lambda \) — Correct, as this is the standard wave equation.
Option (2): \( \gamma = \frac{V}{\lambda} \) — Correct, as this is a valid rearrangement of the wave equation.
Option (3): \( \lambda = \frac{V}{\gamma} \) — Correct, as this is another valid rearrangement of the wave equation.
Option (4): All of these — Correct, as all three equations are valid relationships derived from the wave equation. Step 3: Final Answer.
\[ \boxed{(4) \quad \text{All of these}} \]