A wave on a string is described by D (x,t) = (2.00 cm) ✕ sin [(12.57 rad/m)x ─ (638 rad/s) t], where x is in m and t in s. The linear density of the string is 5.00 g/m. What are
c. The maximum speed of a point on the string?
Verified step by step guidance
1
Identify the amplitude (A) and the angular frequency (\(\omega\)) from the wave equation \(D(x,t) = A \sin(kx - \omega t)\). In this case, \(A = 2.00\, \text{cm}\) and \(\omega = 638\, \text{rad/s}\).
Convert the amplitude from centimeters to meters for consistency in units. Since 1 cm = 0.01 m, multiply the amplitude by 0.01.
The maximum speed of a point on the string (\(v_{\text{max}}\)) is given by the product of the amplitude in meters and the angular frequency, i.e., \(v_{\text{max}} = A \omega\).
Substitute the values of \(A\) in meters and \(\omega\) into the formula to calculate \(v_{\text{max}}\).
Ensure the final answer is in meters per second (m/s), as this is the standard unit for speed in the International System of Units (SI).