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 become triple its original value.
It will become triple its original value.
It will become one third of its original value.
It will become one third of its original value.
It will depend on the speed of the wave.
It will depend on the speed of the wave.
It will remain constant.
Responses
It will become triple its original value.
It will become triple its original value.
It will become one third of its original value.
It will become one third of its original value.
It will depend on the speed of the wave.
It will depend on the speed of the wave.
It will remain constant.
Answers
GPT-4o mini
The correct response is:
**It will become one third of its original value.**
This is based on the relationship defined by the wave equation:
\[ v = f \lambda \]
where \( v \) is the speed of the wave, \( f \) is the frequency, and \( \lambda \) is the wavelength.
If the wavelength is tripled (\( \lambda' = 3\lambda \)), and assuming the wave speed \( v \) remains constant, the frequency (\( f' \)) can be expressed as:
\[ f' = \frac{v}{\lambda'} = \frac{v}{3\lambda} = \frac{1}{3} \cdot \frac{v}{\lambda} = \frac{f}{3} \]
Thus, if the wavelength triples, the frequency becomes one third of its original value.
**It will become one third of its original value.**
This is based on the relationship defined by the wave equation:
\[ v = f \lambda \]
where \( v \) is the speed of the wave, \( f \) is the frequency, and \( \lambda \) is the wavelength.
If the wavelength is tripled (\( \lambda' = 3\lambda \)), and assuming the wave speed \( v \) remains constant, the frequency (\( f' \)) can be expressed as:
\[ f' = \frac{v}{\lambda'} = \frac{v}{3\lambda} = \frac{1}{3} \cdot \frac{v}{\lambda} = \frac{f}{3} \]
Thus, if the wavelength triples, the frequency becomes one third of its original value.