Question
If the wavelength of a wave in a particular medium is tripled, what will happen to the frequency of the wave?(1 point)
Responses
It will depend on the speed of the wave.
It will depend on the speed of the wave.
It will become triple its original value.
It will become triple its original value.
It will remain constant.
It will remain constant.
It will become one third of its original value.
Responses
It will depend on the speed of the wave.
It will depend on the speed of the wave.
It will become triple its original value.
It will become triple its original value.
It will remain constant.
It will remain constant.
It will become one third of its original value.
Answers
GPT-4o mini
The correct response is:
**It will become one third of its original value.**
This is because the relationship between the speed (v), frequency (f), and wavelength (λ) of a wave is given by the equation:
\[ v = f \cdot λ \]
If the wavelength is tripled (λ becomes 3λ), and assuming the speed of the wave in that medium remains constant, the frequency will decrease. Specifically, since \( v \) is constant, if \( λ \) increases by a factor of 3, then \( f \) must decrease by a factor of 3 to maintain the equation:
\[ f = \frac{v}{λ} \]
Thus, if \( λ \) becomes 3λ, then:
\[ f' = \frac{v}{3λ} = \frac{1}{3}f \]
So, the frequency becomes one third of its original value.
**It will become one third of its original value.**
This is because the relationship between the speed (v), frequency (f), and wavelength (λ) of a wave is given by the equation:
\[ v = f \cdot λ \]
If the wavelength is tripled (λ becomes 3λ), and assuming the speed of the wave in that medium remains constant, the frequency will decrease. Specifically, since \( v \) is constant, if \( λ \) increases by a factor of 3, then \( f \) must decrease by a factor of 3 to maintain the equation:
\[ f = \frac{v}{λ} \]
Thus, if \( λ \) becomes 3λ, then:
\[ f' = \frac{v}{3λ} = \frac{1}{3}f \]
So, the frequency becomes one third of its original value.