Question

The wave function of a standing wave is y(x,t)= 4.44 mmsin [(32.5 rad/m) x] sin [(754rad/s)t].

Part A: For the two traveling waves that make up this standing wave, find the amplitude.

Part B: For the two traveling waves that make up this standing wave, find the wavelength.

Part C: For the two traveling waves that make up this standing wave, find the frequency

Part D: For the two traveling waves that make up this standing wave, find the wave speed

Answer 1

The amplitude of the traveling waves is 4.44 mm. The wavelength is approximately 0.194 m. The frequency is approximately 120 Hz. The wave speed is approximately 23.5 m/s.

Step-by-step explanation:

Part A: The amplitude of a wave is the maximum displacement from the equilibrium position. In this case, the amplitude of each traveling wave is 4.44 mm.

Part B: The wavelength of a wave is the distance between two adjacent crests or troughs. For the traveling waves in the standing wave, the wavelength is given by λ = 2π/k, where k is the wave number. In this case, the wave number is 32.5 rad/m, so the wavelength is approximately 0.194 m.

Part C: The frequency of a wave is the number of cycles per unit time. For the traveling waves in the standing wave, the frequency is given by f = w/2π, where w is the angular frequency. In this case, the angular frequency is 754 rad/s, so the frequency is approximately 120 Hz.

Part D: The wave speed of a wave is given by v = λf, where λ is the wavelength and f is the frequency. In this case, the wave speed is approximately 23.5 m/s.

Answer 2

The amplitude of the traveling waves is 4.44 mm. The wavelength is approximately 0.194 m. The frequency is approximately 120 Hz. The wave speed is approximately 23.5 m/s.

Step-by-step explanation:

Part A: The amplitude of a wave is the maximum displacement from the equilibrium position. In this case, the amplitude of each traveling wave is 4.44 mm.

Part B: The wavelength of a wave is the distance between two adjacent crests or troughs. For the traveling waves in the standing wave, the wavelength is given by λ = 2π/k, where k is the wave number. In this case, the wave number is 32.5 rad/m, so the wavelength is approximately 0.194 m.

Part C: The frequency of a wave is the number of cycles per unit time. For the traveling waves in the standing wave, the frequency is given by f = w/2π, where w is the angular frequency. In this case, the angular frequency is 754 rad/s, so the frequency is approximately 120 Hz.

Part D: The wave speed of a wave is given by v = λf, where λ is the wavelength and f is the frequency. In this case, the wave speed is approximately 23.5 m/s.