Question

there is a mathematical relationship between wave speed, wavelength, and frequency:
wave speed = wavelength $cdot$ 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.
wavelength (ft.) | frequency (hz)
6 | 3
9 |
18 |
complete the sentence about a wave moving at constant speed.
if the waves wavelength increases, then its frequency ______.
stays the same
increases
decreases

Explanation:

Step1: Rearrange the wave speed formula

We know wave speed $v = \lambda \cdot f$, so solve for frequency:
$f = \frac{v}{\lambda}$
where $v=18$ ft/s (constant wave speed)

Step2: Calculate frequency for $\lambda=9$ ft

Substitute $\lambda=9$ into the formula:
$f = \frac{18}{9} = 2$

Step3: Calculate frequency for $\lambda=18$ ft

Substitute $\lambda=18$ into the formula:
$f = \frac{18}{18} = 1$

Step4: Analyze wavelength-frequency relationship

Since $f = \frac{v}{\lambda}$ and $v$ is constant, as $\lambda$ increases, $f$ must decrease.

Answer:

Completed Table:

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

Completed Sentence:

If the wave's wavelength increases, then its frequency decreases.