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.