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. 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: Find the formula for frequency

Given wave speed \(v=\text{wavelength}\times\text{frequency}\), so \(\text{frequency}=\frac{v}{\text{wavelength}}\)

Step2: Calculate frequency for wavelength \(15\) cm

Since \(v = 30\) cm/s, when \(\text{wavelength}=15\) cm, \(\text{frequency}=\frac{30}{15}=2\) Hz

Step3: Calculate frequency for wavelength \(20\) cm

When \(\text{wavelength}=20\) cm, \(\text{frequency}=\frac{30}{20}=1.5\) Hz

Step4: Analyze the relationship between wavelength and frequency

Since \(v=\text{wavelength}\times\text{frequency}\) and \(v\) is constant (\(v = 30\) cm/s), if \(\text{wavelength}\) increases, then \(\text{frequency}\) must decrease (because \(v\) is fixed, and \(\text{frequency}=\frac{v}{\text{wavelength}}\))

Answer:

For the table:

• When wavelength is \(15\) cm, frequency is \(2\) Hz
• When wavelength is \(20\) cm, frequency is \(1.5\) Hz

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