Question

Predict what will happen to the wavelength and speed of your coiled spring wave when you increase its frequency and amplitude. Make sure you give an explanation backing up your statement.

Answer 1

The wavelength of a wave is expressed as:

$\lambda=\frac{V}{f}$

Where:

$\lambda$ is the wavelength of the wave

$V$ is the velocity of the wave

$f$ is the frequency of the wave  

According to the expression above, the wavelength is directly proportional to the velocity (this means that if the velocity increases, the wavelength will also increase) and inversely proportional to the frequency (this means that if the frequency increases the wavelength will decrease, and vice versa).  

Then, if the frequency $f$ of the wave increases, the velocity (in this case called speed) and the wavelength will decrease.

Another way to approach this is:

In a division, if the denominator is greater than the numerator, the result will tend to be smaller.

Now, going back to the expression above, we are able to see that the wavelength $\lambda$ does not depend on the Amplitude. Hence, if we increase the Amplitude, the wavelength will not change, it will not be affected.