if two waves are traveling at the same speed along the x axis will the one with the longer wavelength have the larger or smaller freq ? explain in terms of the number of wavelengths that pass a given point on the x axis in 1 sec

My answer: smaller

But how do I explain interns of the number of wavelengths that pass a given pouring on the x axis in 1 sec?

Give an example.

To explain in terms of the number of wavelengths that pass a given point on the x-axis in 1 second, we can make use of the wave equation:

speed = frequency × wavelength

Since both waves are traveling at the same speed along the x-axis, we can say that their speeds are equal.

If the wavelength of one wave is longer, it means that it takes a longer distance for one complete wave cycle to pass a given point on the x-axis. This results in a lower frequency because fewer wavelengths will pass that point in 1 second.

On the other hand, if the wavelength is shorter, it means that it takes a shorter distance for one complete wave cycle to pass a given point. This results in a higher frequency because more wavelengths will pass that point on the x-axis in 1 second.

Therefore, the wave with the longer wavelength will have a smaller frequency, as fewer wavelengths will pass a given point on the x-axis in 1 second.

To explain in terms of the number of wavelengths that pass a given point on the x-axis in one second, you need to understand the relationship between wavelength and frequency. Wavelength (λ) is the distance between two consecutive points on a wave that are in phase with each other, while frequency (f) measures how many complete wavelengths pass a point in one second.

The formula that relates wavelength and frequency is:

speed = wavelength x frequency

Since both waves are traveling at the same speed along the x-axis, their speeds are equal. Therefore, we can equate their wavelengths and frequencies:

wavelength₁ x frequency₁ = wavelength₂ x frequency₂

Given that wavelength₂ is longer than wavelength₁, we can rewrite this equation as:

wavelength₁ x frequency₁ = (wavelength₁ + Δλ) x frequency₂

where Δλ represents the difference in wavelengths between the two waves.

Now, let's assume that both waves take the same amount of time to pass a given point on the x-axis (one second). This means that the frequencies of the two waves are the same:

frequency₁ = frequency₂

Substituting this into our previous equation, we get:

wavelength₁ x frequency₁ = (wavelength₁ + Δλ) x frequency₁

Now, rearranging the equation, we can solve for Δλ:

wavelength₁ x frequency₁ - wavelength₁ x frequency₁ = Δλ x frequency₁

0 = Δλ x frequency₁

Therefore, Δλ = 0, which means there is no change in wavelength. This implies that the longer wavelength (wavelength₂) has a smaller frequency (frequency₂) compared to the shorter wavelength (wavelength₁) with frequency₁.

In conclusion, when two waves are traveling at the same speed along the x-axis, the one with the longer wavelength will have a smaller frequency.