Question

If the wavelength of a wave in a particular medium is tripled, what will happen to the frequency of
the wave? (1 point)

It will depend on the speed of the wave.

It will become one third of its original value.

It will remain constant.

It will become triple its original value.

Answer 1

The frequency of a wave is inversely related to its wavelength when the speed of the wave is constant. This relationship is described by the formula:

\[ v = f \lambda \]

where \( v \) is the speed of the wave, \( f \) is the frequency, and \( \lambda \) is the wavelength. If the wavelength \( \lambda \) is tripled (\( \lambda' = 3\lambda \)), we can rearrange the formula to find the new frequency:

Given that the speed \( v \) remains constant:

\[ v = f' \lambda' \]
\[ v = f \lambda \]

Since \( \lambda' = 3\lambda \), we have:

\[ v = f' (3\lambda) \]

Setting the two expressions for velocity equal:

\[ f \lambda = f' (3\lambda) \]

We can cancel \( \lambda \) (assuming \( \lambda \) is not zero):

\[ f = 3f' \]

Now, solving for the new frequency \( f' \):

\[ f' = \frac{f}{3} \]

Thus, the new frequency will be one third of its original value.

So the answer is:

**It will become one third of its original value.**