Question

A 1.70 m string of weight 0.0125 n is tied to the ceiling at its upper end, and the lower end supports a weight w. ignore the very small variation in tension along the length of the string that is produced by the weight of the string. when you pluck the string slightly, the waves traveling up the string obey the equation: y(x,t)=(8.50mm)cos(172rad/m * x − 4830rad/s * t) assume that the tension of the string is constant and equal to w. how much time does it take a pulse to travel the full length of the string?

Answer 1

To determine the time it takes for a pulse to travel the full length of the string, we need to find the velocity of the wave on the string.

The equation for the wave on the string is given by: y(x, t) = (8.50 mm) * cos(172 rad/m * x - 4830 rad/s * t)

Comparing this equation to the general wave equation y(x, t) = A * cos(kx - ωt), we can see that the angular wave number (k) is equal to 172 rad/m and the angular frequency (ω) is equal to 4830 rad/s.

The velocity of the wave on the string can be determined using the formula:

v = ω / k

Substituting the given values, we can calculate the velocity:

v = 4830 rad/s / 172 rad/m
v ≈ 28.14 m/s

Now, to find the time it takes for a pulse to travel the full length of the string, we divide the length of the string by the velocity:

Length of string = 1.70 m

Time = Length of string / Velocity
Time = 1.70 m / 28.14 m/s
Time ≈ 0.0604 s

Therefore, it takes approximately 0.0604 seconds for a pulse to travel the full length of the string.