Marco is conducting an experiment. He knows the wave that he is working with has a wavelength of 32.4 cm. If he measures the frequency as 3 hertz, which statement about the wave is accurate?

The wave has traveled 32.4 cm in 3 seconds.
The wave has traveled 32.4 cm in 9 seconds.
The wave has traveled 97.2 cm in 3 seconds.
The wave has traveled 97.2 cm in 1 secondMarco is conducting an experiment. He knows the wave that he is working with has a wavelength of 32.4 cm. If he measures the frequency as 3 hertz, which statement about the wave is accurate?

The wave has traveled 32.4 cm in 3 seconds.
The wave has traveled 32.4 cm in 9 seconds.
The wave has traveled 97.2 cm in 3 seconds.
The wave has traveled 97.2 cm in 1 second

First of all, wavelength is the minimum distance between two successive points on the wave that are in the same state of vibration. It is expressed in units of length.

On the other side, frequency is the number of vibrations that occur in a unit of time. Its unit is s⁻¹ or hertz (Hz).

Finally, the propagation speed is the speed with which the wave propagates in the medium, that is, it is the magnitude that measures the speed at which the wave disturbance propagates along its displacement.

The propagation speed relate the wavelength (λ) and the frequency (f) inversely proportional using the following equation:

v = f×λ

Therefore, the previous expression establishes an inversely proportional relationship between the frequency and the wavelength: The higher the frequency, the lower the wavelength and when the frequency is lower, the greater the wavelength.

This case

In this case, you know:

v=?
f= 3 Hz
λ= 32.4 cm

Replacing in the definition of propagation speed:

v= 3 Hz× 32.4 cm

Solving:

v= 97.2 cm/s

In summary, the propagation speed is 97.2 cm/s. This indicates that the wave has traveled 97.2 cm in 1 second.

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