A rope of total mass m and length L is suspended vertically. Analysis shows that for short transverse pulses, the waves above a short distance from the free end of the rope can be represented to a good approximation by the linear wave equation discussed in Section 16.5. Show that a transverse pulse travels the length of the rope in a time interval that is given approximately by Δ t = 2 L / g . Suggestion: First find an expression for the wave speed at any point a distance x from the lower end by considering the rope’s tension as resulting from the weight of the segment below that point.
A rope of total mass m and length L is suspended vertically. Analysis shows that for short transverse pulses, the waves above a short distance from the free end of the rope can be represented to a good approximation by the linear wave equation discussed in Section 16.5. Show that a transverse pulse travels the length of the rope in a time interval that is given approximately by Δ t = 2 L / g . Suggestion: First find an expression for the wave speed at any point a distance x from the lower end by considering the rope’s tension as resulting from the weight of the segment below that point.
Solution Summary: The author explains that the transverse pulse travels the length of the rope in a time interval that is given approximately by Delta tapprox 2sqrt
A rope of total mass m and length L is suspended vertically. Analysis shows that for short transverse pulses, the waves above a short distance from the free end of the rope can be represented to a good approximation by the linear wave equation discussed in Section 16.5. Show that a transverse pulse travels the length of the rope in a time interval that is given approximately by
Δ
t
=
2
L
/
g
. Suggestion: First find an expression for the wave speed at any point a distance x from the lower end by considering the rope’s tension as resulting from the weight of the segment below that point.
If a wave that is traveling is described by
y(x,t) = (0.00327 m) sin (72.1 x +2.27 t),
where the standard SI units are used (72.1 rad/m and 2.72 rad/s), then what is the transverse acceleration of the string element at x = 25.2 cm and t = 19.8 s?
If a wave that is traveling is described by
y(x,t) = (0.00327 m) sin (72.1 x +2.27 t),
where the standard SI units are used (72.1 rad/m and 2.72 rad/s), then what is the transverse velocity of the string element at x = 25.2 cm and t = 19.8 s?
A standing wave on a stretched string with a tension force F_T and of length L = 2 m has the following equation: y(x,t) = 0.1 sin(2πx) cos(100πt). How many loops would appear on the string if the velocity is reduced by a factor of 3 while the frequency is held constant?
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Wave Speed on a String - Tension Force, Intensity, Power, Amplitude, Frequency - Inverse Square Law; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=vEzftaDL7fM;License: Standard YouTube License, CC-BY