With what tension must a rope with length 2.10m and mass 0.115kg be stretched for transverse waves of frequency 39.0hz to have a wavelength of 0.790m ?
Hey just finished this question on mastering physics.
The velocity of a wave is defined as wavelength*frequency.
it is also defined as sqrt(Tension/(mass/rope length)).
Set the two definitions equal to each other and solve for the Tension and you should have your answer!
To find the tension in the rope, we can use the formula for the velocity of a transverse wave on a rope:
velocity = sqrt(tension / linear density)
The linear density of the rope can be found using the formula:
linear density = mass / length
First, let's calculate the linear density:
linear density = mass / length
= 0.115kg / 2.10m
≈ 0.0548 kg/m
Next, we'll calculate the velocity of the wave:
velocity = sqrt(tension / linear density)
To find the tension, we rearrange the formula to solve for tension:
tension = velocity^2 * linear density
Substituting the given values:
velocity = frequency * wavelength
= 39.0 Hz * 0.790 m
= 30.71 m/s
tension = (30.71 m/s)^2 * 0.0548 kg/m
≈ 52.31 N
Therefore, the rope must be stretched with a tension of approximately 52.31 Newtons for the transverse waves to have a wavelength of 0.790m.