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 become one third of its original value. it will become triple its original value. it will depend on the speed of the wave. it will remain constant.

Explanation:

Step1: Recall wave speed formula

The formula relating wave speed (\(v\)), wavelength (\(\lambda\)), and frequency (\(f\)) is \(v = \lambda f\). In a particular medium, the wave speed \(v\) remains constant (since the medium doesn't change).

Step2: Analyze the relationship between \(\lambda\) and \(f\)

From \(v=\lambda f\), we can rearrange to solve for frequency: \(f=\frac{v}{\lambda}\). Since \(v\) is constant (same medium), frequency \(f\) is inversely proportional to wavelength \(\lambda\) (i.e., \(f\propto\frac{1}{\lambda}\)).

Step3: Apply the change in wavelength

If the wavelength \(\lambda\) is tripled, let the original wavelength be \(\lambda_1\) and new wavelength be \(\lambda_2 = 3\lambda_1\). Let original frequency be \(f_1=\frac{v}{\lambda_1}\) and new frequency be \(f_2=\frac{v}{\lambda_2}\). Substitute \(\lambda_2 = 3\lambda_1\) into \(f_2\): \(f_2=\frac{v}{3\lambda_1}=\frac{1}{3}\times\frac{v}{\lambda_1}=\frac{1}{3}f_1\). So the frequency becomes one - third of its original value.

Answer:

It will become one third of its original value.