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.
eli creates a wave with a constant speed of 30 centimeters per second. as he changes the wavelength, how does the frequency change? complete the table.
write your answers as whole numbers or decimals.
wavelength (cm) | frequency (hz)
10 | 3
15 |
20 |
complete the sentence about a wave moving at constant speed.
if the waves wavelength increases, then its frequency ______.
decreases stays the same increases

Explanation:

Step1: Rearrange wave speed formula

$\text{frequency} = \frac{\text{wave speed}}{\text{wavelength}}$

Step2: Calculate frequency for 15 cm

$\text{frequency} = \frac{30}{15} = 2$

Step3: Calculate frequency for 20 cm

$\text{frequency} = \frac{30}{20} = 1.5$

Step4: Analyze wavelength-frequency relationship

Since $\text{frequency} \propto \frac{1}{\text{wavelength}}$ (constant speed), as wavelength increases, frequency decreases.

Answer:

Completed Table:

wavelength (cm)	frequency (Hz)
15	2
20	1.5

Completed Sentence:

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