# Physics conceptual question

#### MC789

##### Full Member
2+ Year Member
as I'm doing practice physics questions, I keep getting confused regarding the relationship between wave velocity, wavelength, and frequency. I originally thought that waves with higher frequency and lower wavelength would travel faster because they finish the wave cycle in a shorter amount of time. but as I'm looking at the answer key, many answers say waves with the higher wavelength travel faster. can someone explain please? and under what conditions does velocity, wavelength, or frequency of a wave stay constant?

Vendor
2+ Year Member
Hi, MC789--

If you ever forget the relationship, just remember the units. You know velocity, v, is measured in m/s. You know wavelength, lambda, is measured in m. You know frequency, f, is measured s^-1 (called a hertz). Therefore, v = (lambda)(f) = (m)(s^-1) = m/s. Velocity = wavelength x frequency.

In a vacuum, the velocity is constant (called c) for all electromagnetic radiation (c = 3.00 x 10^8 m/s). However, when it enters a different medium (like glass or water), only the frequency remains constant. The rate the waves enter must equal the rate the waves exit the medium. Therefore, frequency is constant, and from above, we then know f = v / lambda.

We know that v in a medium is slower than v in a vacuum (v < c). If velocity went down but frequency remained constant, what happens to the wavelength? It must get shorter (smaller value). Remember, frequency = velocity / wavelength.

A shorter wavelength will have a lower velocity through a medium. For example, blue light travels through a medium slower than red light (it has a shorter wavelength). Red light has a longer wavelength and a faster velocity (than blue) in a medium. However, to repeat, they all have the same velocity in a vacuum.

As a side note, because blue light travels slower than red light in a medium, blue light will refract to a greater degree than red light.

Fortunately, we can treat air like a vacuum where velocity in air = c for them all.

Happy Studying!

1 user

#### MC789

##### Full Member
2+ Year Member
Hi, MC789--

If you ever forget the relationship, just remember the units. You know velocity, v, is measured in m/s. You know wavelength, lambda, is measured in m. You know frequency, f, is measured s^-1 (called a hertz). Therefore, v = (lambda)(f) = (m)(s^-1) = m/s. Velocity = wavelength x frequency.

In a vacuum, the velocity is constant (called c) for all electromagnetic radiation (c = 3.00 x 10^8 m/s). However, when it enters a different medium (like glass or water), only the frequency remains constant. The rate the waves enter must equal the rate the waves exit the medium. Therefore, frequency is constant, and from above, we then know f = v / lambda.

We know that v in a medium is slower than v in a vacuum (v < c). If velocity went down but frequency remained constant, what happens to the wavelength? It must get shorter (smaller value). Remember, frequency = velocity / wavelength.

A shorter wavelength will have a lower velocity through a medium. For example, blue light travels through a medium slower than red light (it has a shorter wavelength). Red light has a longer wavelength and a faster velocity (than blue) in a medium. However, to repeat, they all have the same velocity in a vacuum.

As a side note, because blue light travels slower than red light in a medium, blue light will refract to a greater degree than red light.

Fortunately, we can treat air like a vacuum where velocity in air = c for them all.

Happy Studying!

Thank you!!

1 user
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