Question

if wave x has a higher frequency than wave y, how does the wavelength of wave x compare to wave y?
the wavelength cannot be determined from frequency alone.
wave x has the same wavelength as wave y.
wave x has a shorter wavelength than wave y.
wave x has a longer wavelength than wave y.

Explanation:

Step1: Recall the wave formula

The formula for waves is \(v = f\lambda\), where \(v\) is the wave - speed, \(f\) is the frequency, and \(\lambda\) is the wavelength.

Step2: Analyze the relationship between frequency and wavelength

If we assume the wave - speed \(v\) is constant (for example, in a vacuum for electromagnetic waves or in a homogeneous medium for mechanical waves), then \(\lambda=\frac{v}{f}\). This shows an inverse relationship between wavelength \(\lambda\) and frequency \(f\).

Step3: Compare wavelengths based on frequencies

Given that \(f_X>f_Y\). Using the formula \(\lambda=\frac{v}{f}\), when \(v\) is constant, if \(f\) increases, \(\lambda\) decreases. So, \(\lambda_X<\lambda_Y\)

Answer:

Wave X has a shorter wavelength than Wave Y.