The wave speed on a string is 148.9 m/s when the tension is 73.4 N. What tension will give a speed 184.9 m/s?
Wave speed is proportional to the square root of tension. You want to increase the wave speed by a factor
184.9/148.9 = 1.242
Tension must increase by the square of that factor.
To calculate the tension required to produce a wave speed of 184.9 m/s, we can use the formula for wave speed on a string:
Wave speed = √(tension / linear density)
Given that the wave speed is 148.9 m/s and the tension is 73.4 N, we can rearrange the formula to solve for the linear density:
148.9 m/s = √(73.4 N / linear density)
Squaring both sides of the equation gives:
(148.9 m/s)^2 = 73.4 N / linear density
Now, let's rearrange the equation to solve for the linear density:
linear density = 73.4 N / (148.9 m/s)^2
linear density ≈ 0.333 kg/m
Now, we can use the same formula to calculate the tension required to achieve a wave speed of 184.9 m/s:
184.9 m/s = √(tension / 0.333 kg/m)
Squaring both sides of the equation gives:
(184.9 m/s)^2 = tension / 0.333 kg/m
Now, let's rearrange the equation to solve for tension:
tension = (184.9 m/s)^2 * 0.333 kg/m
tension ≈ 10,334.71 N
Therefore, the tension required to achieve a wave speed of 184.9 m/s is approximately 10,334.71 N.