The speed of a transverse wave on a rope when the mass is increased can be calculated using the formula: Speed = sqrt(Tension / linear mass density). When the mass is increased from 1.50 kg to 3.00 kg, the speed of the wave on the rope increases from 9.47 m/s to 15.2 m/s.
Step-by-step explanation:
To find the speed of a transverse wave on a rope when the mass is increased, we can use the formula:
Speed = sqrt(Tension / linear mass density)
where Tension is the force acting on the rope and linear mass density is the mass per unit length of the rope.
Given that the linear mass density of the rope is 0.0680 kg/m and the tension is calculated using the formula:
Tension = mass * gravity
where mass is the mass at the end of the rope and gravity is the acceleration due to gravity.
So, the tension when the mass is 1.50 kg is:
Tension = 1.50 kg * 9.8 m/s^2 = 14.7 N
Using this value in the formula for speed gives:
Speed = sqrt(14.7 N / 0.0680 kg/m) = 9.47 m/s
When the mass is increased to 3.00 kg, the tension will also increase. The new tension can be calculated in the same way:
Tension = 3.00 kg * 9.8 m/s^2 = 29.4 N
Using this value in the formula for speed, we can find the new speed:
Speed = sqrt(29.4 N / 0.0680 kg/m) = 15.2 m/s
The probable question can be: Part C One end of a horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates the rope transversely at 140 Hz. The other end passes over a pulley and supports a 1.50 kg mass. The linear mass density of the rope is 0.0680 kg/m. What is the speed of a transverse wave on the rope if the mass were increased to 3.00 kg? Express your answer with the appropriate units. MÅ ? V= Value Units Submit Request Answer Part D What is the wavelength of a transverse wave on the rope if the mass were increased to 3.00 kg? Express your answer with the appropriate units. μΑ ? l= Value Units