# Math Help - [SOLVED] Sine wave relationship

1. ## [SOLVED] Sine wave relationship

Hello,

Can someone explain to me why the answer to the following question is λf=v? (λ is wavelength, f is frequency, v is speed)

Question: What is the relationship between the wavelength and frequency of a sine wave?

Answer:λf=v

Thank you in advance!

2. Originally Posted by sparky
Hello,

Can someone explain to me why the answer to the following question is λf=v? (λ is wavelength, f is frequency, v is speed)

Question: What is the relationship between the wavelength and frequency of a sine wave?

Answer:λf=v

Thank you in advance!

Wavelength $\lambda$ is literally translated to the length of your sine curve, as seen above, generally it is in units of length. (ie. cm)

Frequency is the inverse of how many cycles of sine curves per unit time, generally it is units of inverse time or Hertz. (ie. $\frac{1}{min}$ or Hz).

If you do unit analysis, you will notice that speed is in units of $\frac{length}{time}$. This is exactly the product of wavelength $\lambda$ and frequency $f$:

$\lambda (cm) \cdot f \left(\frac{1}{min}\right) = v \left(\frac{cm}{min}\right)$

3. ## Sine wave

Hello sparky
Originally Posted by sparky
Hello,

Can someone explain to me why the answer to the following question is λf=v? (λ is wavelength, f is frequency, v is speed)

Question: What is the relationship between the wavelength and frequency of a sine wave?

Answer:λf=v

Thank you in advance!
Imagine you're standing on a bridge watching a long train passing underneath. Each truck is (let's say) 6 m long, and you count 100 trucks pass by in one minute. How fast is the train travelling?

Well, as one truck passes by, the train moves forward 6m. So if 100 trucks go by, it must move 6 x 100 = 600m. And if it does this in one minute, it must be travelling at a speed of 600m per minute. (You don't have to use minutes, of course; any other unit of time will work in just the same way.)

With a sine wave, the wavelength, $\lambda$, is like the length of the truck: it's the distance between corresponding points on two adjacent cycles of the wave. The frequency, $f$, is like the number of trucks passing by a fixed point in a given unit of time, except that it's the number of cycles, instead of trucks. And you'll see that we simply multiplied the length of each truck by the number of trucks that went by in one minute to get the speed of the train. Well, that's what you do with a sine wave to get its speed, $v$: multiply the wavelength by the frequency.

So you get the equation $v = \lambda f$.

Does that help?

Grandad

4. Thank you very much Star Tenshi and Grandad. Your answers were very helpful and I understand clearly now!