AP Physics 2 - Wave Characteristics

A wave of wavelength 0.1 meters is traveling through a medium with a speed of 2 m/s. The wave's frequency is 50 Hz. Determine the amplitude, period, angular frequency, and wave number of this wave. Explain each step in detail and provide the final answers.

Solution: Given: Wavelength (λ) = 0.1 m Wave speed (v) = 2 m/s Frequency (f) = 50 Hz

To find: Amplitude (A), Period (T), Angular frequency (ω), Wave number (k)

Step 1: Determine the amplitude (A) The amplitude of a wave represents its maximum displacement from the equilibrium position. However, in this question, the amplitude is not mentioned explicitly. Therefore, the amplitude cannot be determined with the given information. We will consider it as unknown.

Step 2: Derive the period (T) The period of a wave represents the time taken for one complete oscillation or cycle. It can be calculated using the formula: T = 1 / f where f is the frequency.

Using the given frequency, we can substitute the value into the equation: T = 1 / 50 Hz = 0.02 s

Step 3: Calculate the angular frequency (ω) The angular frequency of a wave is given by the formula: ω = 2πf where f is the frequency.

Substituting the given frequency, we have: ω = 2π × 50 Hz = 100π rad/s

Step 4: Compute the wave number (k) The wave number represents the number of wavelengths per unit distance (usually per meter) and is given by the formula: k = 2π / λ where λ is the wavelength.

Substituting the given wavelength, we have: k = 2π / 0.1 m = 20π rad/m

Step 5: Final summary Amplitude (A) - Unknown (since it is not stated) Period (T) - 0.02 s Angular frequency (ω) - 100π rad/s Wave number (k) - 20π rad/m

Therefore, the amplitude cannot be determined from the given information. The period is 0.02 seconds, the angular frequency is 100π rad/s, and the wave number is 20π rad/m.