Question

there is a mathematical relationship between wave speed, wavelength, and frequency:
wave speed = wavelength · frequency
if the medium a wave moves through does not change, wave speed is constant.
maya creates a wave with a constant speed of 18 feet per second. as she changes the wavelength, how does the frequency change? complete the table.
write your answers as whole numbers or decimals.
complete the sentence about a wave moving at constant speed.
if the waves wavelength increases, then its frequency ______.
decreases increases stays the same

Explanation:

Step1: Find the formula for frequency

Given \(v = \lambda\cdot f\) (where \(v\) is wave - speed, \(\lambda\) is wavelength, \(f\) is frequency), we can solve for \(f\) as \(f=\frac{v}{\lambda}\).
Since \(v = 18\) ft/s (constant).

Step2: Calculate frequency for \(\lambda = 9\)

Substitute \(\lambda=9\) into \(f=\frac{v}{\lambda}\), we get \(f=\frac{18}{9}\).
\(f = 2\)

Step3: Calculate frequency for \(\lambda = 18\)

Substitute \(\lambda = 18\) into \(f=\frac{v}{\lambda}\), we get \(f=\frac{18}{18}\).
\(f = 1\)

Step4: Analyze the relationship between wavelength and frequency

From \(f=\frac{v}{\lambda}\) (with \(v\) constant), when \(\lambda\) increases (since \(v\) is a non - zero constant), \(f\) decreases. For example, when \(\lambda\) goes from \(6\) to \(9\) (an increase), \(f\) goes from \(3\) to \(2\) (a decrease); when \(\lambda\) goes from \(9\) to \(18\) (an increase), \(f\) goes from \(2\) to \(1\) (a decrease)

Answer:

wavelength (ft.)	frequency (Hz)
9	2
18	1

If the wave's wavelength increases, then its frequency \(decreases\)