Question 408: Waves

Question

Velocity of sound waves in air is '$$\mathrm{V}$$' $$\mathrm{m} / \mathrm{s}$$. For a particular sound wave in air, path difference of 'x' $$\mathrm{cm}$$ is equivalent to phase difference $$n \pi$$. The frequency of this wave is

Accepted Answer

To find the frequency of the sound wave given the relationship between the path difference and phase difference, let's start by understanding the relationship between these quantities.
The path difference (x) and the phase difference ($$n \pi$$) for a wave can be related via the wavelength ($$\lambda$$) of the wave. The path difference corresponding to a phase difference of $$2\pi$$ radians is one wavelength, i.e., $$x = \lambda$$ when the phase difference is $$2\pi$$.
Given that the path difference $ x $ is equivalent to a phase difference of $$n \pi$$, we can express the path difference as:
$$ x = \frac{n \pi}{2\pi} \lambda $$
Then, simplifying this expression, we get:
$$ x = \frac{n \lambda}{2} $$
Now, rearranging this equation to solve for $$\lambda$$ (wavelength), we have:
$$ \lambda = \frac{2 x}{n} $$
Next, the frequency ($$ f $$) of a wave is related to its wavelength ($$ \lambda $$) and the velocity ($$ V $$) of the wave via the equation:
$$ V = f \lambda $$
Solving for the frequency, we get:
$$ f = \frac{V}{\lambda} $$
Substituting the expression for $$ \lambda $$, we obtain:
$$ f = \frac{V}{\frac{2 x}{n}} $$
Which simplifies to:
$$ f = \frac{V n}{2 x} $$
Thus, the correct option is:
Option C: $$ \frac{V n}{2 x} $$

Answer

$$\frac{V n}{x}$$

Answer

$$\frac{V}{n x}$$

Answer

$$\frac{V n}{2 x}$$

Answer

$$\frac{2 x}{V}$$

Waves

Velocity of sound waves in air is '$\mathrm{V}' \mathrm{m} / \mathrm{s}. For a particular sound wave in air, path difference of 'x' \mathrm{cm} is equivalent to phase difference n \pi$. The frequency of this wave is

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