Consider point 2. Draw in the force ##F## exerted on the small segment of string. What are the x and y components of that force in terms of ##F## and ##\theta_2##?annamal said:
That's not answering my question of how come ##\theta_2## and ##\theta_1## are the angles between the forces. ##\theta_2## could be greater or smaller. ##\theta_2## is the angle due to the y and x quantities but not necessarily the angle for the Fx and Fy quantities.vela said:
vela said:
No, I know that. You're not understanding my question. I attached another image. The blue arrow is one possibility of a resultant force vector in which ##\tan(\theta_2) = \frac{Fy}{Fx}##. The orange arrow is another possibility of a resultant force vectors in which ##\tan(\theta_3) = \frac{Fy}{Fx}##. ##\theta_2 != \theta_3##vela said:
##F_x = F_T## and ##F_y = F_2##vela said:
That's assuming that the string moves in the direction of the applied forcevela said:
The force on each point on the string can only come from adjacent parts of the string. Therefore, the force is always parallel to the string at each point. There is only one possibility for the angle, which is the angle the string itself makes.annamal said:
Can you explain what you mean by adjacent parts?DrClaude said:
Imagine the string as a large number of finite segments. The force on each segment is applied by the two adjacent segments, one on either side.annamal said:
Quite arbitrarily (but obviously the best choice) the tension force has been resolved into a lateral and longitudinal force. This sort of approach is the way we solve hundreds of problems but is probably only valid for small displacements and the diagram exaggerates the scale so that the vectors can be drawn on a diagram.annamal said:
What do you mean by adjacent segments? The x and y components to the net force?PeroK said:
No, a segment is part of the string. The diagram in your original post shows the segment between ##x_1## and ##x_2##.annamal said:
Wave speed on a string under tension is the speed at which a wave travels along a string when it is stretched or under tension. It is affected by the tension in the string and the mass per unit length of the string.
Wave speed on a string under tension is derived using the formula v = √(T/μ), where v is the wave speed, T is the tension in the string, and μ is the mass per unit length of the string. This formula is derived from the wave equation and the principles of string tension.
The wave speed on a string under tension is affected by the tension in the string and the mass per unit length of the string. Increasing the tension or decreasing the mass per unit length will result in a higher wave speed, while decreasing the tension or increasing the mass per unit length will result in a lower wave speed.
The wave speed on a string under tension can be measured by using a stopwatch to time how long it takes for a wave to travel a known distance on the string. The distance and time can then be used to calculate the wave speed using the formula v = d/t, where v is the wave speed, d is the distance, and t is the time.
The relationship between wave speed and frequency on a string under tension is direct. This means that as the wave speed increases, the frequency of the wave also increases. This relationship is described by the formula v = λf, where v is the wave speed, λ is the wavelength, and f is the frequency.