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.
ell 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.
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: Use the formula wave speed = wavelength × frequency

Given wave speed \(v = 30\space cm/s\). The formula can be rewritten as \(frequency=\frac{wave\space speed}{wavelength}\), i.e., \(f=\frac{v}{\lambda}\)

Step2: Calculate frequency for \(\lambda = 15\space cm\)

Substitute \(v = 30\) and \(\lambda=15\) into \(f=\frac{v}{\lambda}\). So \(f=\frac{30}{15}=2\)

Step3: Calculate frequency for \(\lambda = 20\space cm\)

Substitute \(v = 30\) and \(\lambda = 20\) into \(f=\frac{v}{\lambda}\). So \(f=\frac{30}{20}=1.5\)

Step4: Analyze the relationship between wavelength and frequency

Since \(v=\lambda\times f\) (constant \(v\)), \(\lambda\) and \(f\) are inversely - proportional. When \(\lambda\) increases, \(f\) decreases.

Answer:

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

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