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A wave on a string is described by D ( x , t ) = ( 2.0 c m ) s i n [ 2 π ( x / ( 8.4 m ) + t / ( 0.24 s ) + 1 ) ] , where x is in m and t is in s. 1. In what direction is this wave traveling? a. in the positive x-direction b. in the negative x-direction c.in other direction 2. What is the wave speed? 3. What is the frequency? 4. What is the wave number?

User StefanH
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Answer:

Step-by-step explanation:

The wave equation can be written as D(x,t) = Asin(kx - wt + φ), where A is the amplitude, k is the wave number, w is the angular frequency, and φ is the phase constant. The direction of wave propagation is determined by the sign of the wave number, which is given by k = 2π/λ, where λ is the wavelength. In this case, the wave number is positive, which means that the wave is traveling in the positive x-direction.

Answer: a. in the positive x-direction

The wave speed is given by v = λf, where λ is the wavelength and f is the frequency. The wavelength can be determined from the wave number as λ = 2π/k. Therefore, the wave speed is v = f(2π/k). From the equation given, we can see that the wavelength is λ = 8.4 m. Using the relation k = 2π/λ, we get k = 2π/8.4 = 0.75 m^(-1). The frequency is given by f = w/(2π), where w is the angular frequency. From the equation given, we can see that w = 2π/0.24 = 26.18 rad/s. Therefore, the frequency is f = 26.18/(2π) ≈ 4.17 Hz. Substituting these values, we get v = 8.44.17 ≈ 35.03 m/s.

Answer: 35.03 m/s

The frequency is f = w/(2π), where w is the angular frequency. From the equation given, we can see that w = 2π/0.24 = 26.18 rad/s. Therefore, the frequency is f = 26.18/(2π) ≈ 4.17 Hz.

Answer: 4.17 Hz

The wave number is given by k = 2π/λ, where λ is the wavelength. From the equation given, we can see that the wavelength is λ = 8.4 m. Substituting this value, we get k = 2π/8.4 = 0.75 m^(-1).

Answer: 0.75 m^(-1)

User Nicktruesdale
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