A wave has an amplitude of 0.5 m and a frequency of 10 Hz. What is the maximum s

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Question: A wave has an amplitude of 0.5 m and a frequency of 10 Hz. What is the maximum speed of a particle in the wave?

Options:

Correct Answer: 6.28 m/s

Solution:

The maximum speed v_max is given by v_max = ωA, where ω = 2πf. Thus, ω = 2π(10) = 20π and v_max = 20π(0.5) = 10π ≈ 31.42 m/s.

A wave has an amplitude of 0.5 m and a frequency of 10 Hz. What is the maximum speed of a particle in the wave?

A wave has an amplitude of 0.5 m and a frequency of 10 Hz. What is the maximum speed of a particle in the wave?

Step 1: Identify the given values. The amplitude (A) is 0.5 m and the frequency (f) is 10 Hz.
Step 2: Calculate the angular frequency (ω) using the formula ω = 2πf. Substitute f with 10 Hz: ω = 2π(10).
Step 3: Simplify the calculation for ω: ω = 20π.
Step 4: Use the formula for maximum speed (v_max), which is v_max = ωA. Substitute ω with 20π and A with 0.5 m: v_max = 20π(0.5).
Step 5: Simplify the calculation for v_max: v_max = 10π.
Step 6: Calculate the numerical value of v_max: v_max ≈ 31.42 m/s.

Wave Properties – Understanding amplitude, frequency, and their relationship to wave speed.
Angular Frequency – Calculating angular frequency (ω) from frequency (f) using the formula ω = 2πf.
Maximum Speed of Particles in a Wave – Using the formula v_max = ωA to find the maximum speed of particles in a wave.