A long uniform string of mass density 0.1 kg m⁻¹ is stretched with a force of 40 N. One end of the string (x = 0) is oscillating transversely (sinusoidally) with an amplitude of 0.02 m and a period of 0.1 s, so that travelling waves in the +x direction are set up. (a) What is the velocity of the waves? (b) What is their wavelength? (c) If at the driving end (x = 0) the displacement (y) at t = 0 is 0.01 m with dy/dt negative, what is the equation of the travelling waves?
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Question

A long uniform string of mass density 0.1 kg m⁻¹ is stretched with a force of 40 N. One end of the string (x = 0) is oscillating transversely (sinusoidally) with an amplitude of 0.02 m and a period of 0.1 s, so that travelling waves in the +x direction are set up. (a) What is the velocity of the waves? (b) What is their wavelength? (c) If at the driving end (x = 0) the displacement (y) at t = 0 is 0.01 m with dy/dt negative, what is the equation of the travelling waves?

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G1 Physics · Accepted Answer

Step 1: Identify the governing wave relation from the data and preserve the stated boundary/phase conditions. Step 2: Substitute the numerical values with SI units and simplify. Step 3: Compare with the keyed result from the source. Final: D: (a) 20 m s⁻¹; (b) 2 m; (c) y = 0.02 sin(πx − 20πt + π/6).