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A wave is represented by the 38.equation: Y=0.2 sin 0.41 (x-60t),where all distances are measured in cm and time in seconds. Calculate the speed of the wave.

User Aamirkhan
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Final answer:

The speed of the wave represented by the wave function Y=0.2 sin 0.41 (x-60t) is 146.34 cm/s, calculated using the relationship between angular frequency, wave number and wave speed.

Step-by-step explanation:

The student needs to calculate the speed of the wave given by the wave function Y=0.2 sin 0.41 (x-60t). In this function, the number 60, which is the coefficient of t in the argument of the sine function, represents the angular frequency (ω) of the wave, and the variable x represents the position in centimeters. Using the relationship speed = frequency × wavelength, and the fact that the angular frequency (ω) is related to the speed (v) and wave number (k) via the relationship ω = v × k, we can use the other given variable 0.41 as the wave number (k) to find the speed v.

Since the angular frequency ω equals 2π times the frequency (f) and the wave number k equals 2π divided by the wavelength (λ), we can write the following equation:
v = f λ = ω / k = 60 / 0.41 = 146.34 cm/s. Therefore, the speed of the wave is 146.34 cm/s.

User Wellie
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