Question 2 of 23intermediate🔧 ApplyNumerical4 marks

A wave travelling along a string is described by, y(x,t)=0.005sin⁡(80.0x−3.0t)y(x, t) = 0.005 \sin(80.0x - 3.0t), in which the numerical constants are in SI units (0.005 m, 80.0 rad m−1^{-1}, and 3.0 rad s−1^{-1}). Calculate (a) the amplitude, (b) the wavelength, and (c) the period and frequency of the wave. Also, calculate the displacement yy of the wave at a distance x=30.0x = 30.0 cm and time t=20t = 20 s?

(a)
Answer

Amplitude = 0.005 m = 5 mm

(b)
Answer

Wavelength = 7.85 cm

(c)
Answer

Period = 2.09 s, Frequency = 0.48 Hz

Explanation

The given wave equation is compared with the standard form y(x,t) = a sin(kx - ωt). By comparing coefficients, we identify the amplitude, angular wave number k, and angular frequency ω. The wavelength is calculated using λ = 2π/k, and the period using T = 2π/ω. The displacement at given values is calculated by direct substitution.

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