Answer :
To determine which equation correctly calculates wave speed, let's first recall the relationship between wave speed, frequency, and wavelength.
1. Wave speed (v) is the speed at which the wave travels.
2. Frequency (f) is the number of wave cycles that pass a point per unit of time.
3. Wavelength (λ) is the distance between successive crests of a wave.
The correct formula to find the wave speed involves both the frequency and the wavelength. By definition, wave speed is given by:
[tex]\[ v = f \cdot \lambda \][/tex]
This equation states that the wave speed [tex]\(v\)[/tex] is the product of the frequency [tex]\(f\)[/tex] and the wavelength [tex]\(\lambda\)[/tex].
Let's analyze each of the options provided:
A. [tex]\( v = \frac{\lambda}{f} \)[/tex]
- This suggests wave speed is the wavelength divided by frequency, which is incorrect.
B. [tex]\( v = \lambda T \)[/tex]
- Here [tex]\(T\)[/tex] represents the period (the reciprocal of frequency [tex]\(T = \frac{1}{f}\)[/tex]). Therefore, this equation is equivalent to [tex]\( v = \lambda \left( \frac{1}{f} \right)\)[/tex], which simplifies to [tex]\( v = \frac{\lambda}{f} \)[/tex], which is incorrect.
C. [tex]\( v = f \lambda \)[/tex]
- This matches our earlier definition of wave speed. This is a correct formula.
D. [tex]\( v = \frac{f}{\lambda} \)[/tex]
- This suggests that wave speed is the frequency divided by the wavelength, which is incorrect.
Therefore, the correct equation used to calculate wave speed is:
[tex]\[ \boxed{v = f \lambda} \][/tex]
Among the given choices, option C is the correct one.
1. Wave speed (v) is the speed at which the wave travels.
2. Frequency (f) is the number of wave cycles that pass a point per unit of time.
3. Wavelength (λ) is the distance between successive crests of a wave.
The correct formula to find the wave speed involves both the frequency and the wavelength. By definition, wave speed is given by:
[tex]\[ v = f \cdot \lambda \][/tex]
This equation states that the wave speed [tex]\(v\)[/tex] is the product of the frequency [tex]\(f\)[/tex] and the wavelength [tex]\(\lambda\)[/tex].
Let's analyze each of the options provided:
A. [tex]\( v = \frac{\lambda}{f} \)[/tex]
- This suggests wave speed is the wavelength divided by frequency, which is incorrect.
B. [tex]\( v = \lambda T \)[/tex]
- Here [tex]\(T\)[/tex] represents the period (the reciprocal of frequency [tex]\(T = \frac{1}{f}\)[/tex]). Therefore, this equation is equivalent to [tex]\( v = \lambda \left( \frac{1}{f} \right)\)[/tex], which simplifies to [tex]\( v = \frac{\lambda}{f} \)[/tex], which is incorrect.
C. [tex]\( v = f \lambda \)[/tex]
- This matches our earlier definition of wave speed. This is a correct formula.
D. [tex]\( v = \frac{f}{\lambda} \)[/tex]
- This suggests that wave speed is the frequency divided by the wavelength, which is incorrect.
Therefore, the correct equation used to calculate wave speed is:
[tex]\[ \boxed{v = f \lambda} \][/tex]
Among the given choices, option C is the correct one.
