the speed of a wave on a string is 150m/s when the tention is 120n the percentage increase in the tension in order to rise the wave speed by 20% is
To calculate the percentage increase in tension required to raise the wave speed by 20%, we can follow these steps:
Step 1: Determine the initial wave speed.
The initial wave speed on the string is given as 150 m/s.
Step 2: Calculate the increase in wave speed.
To find the increase in wave speed, we multiply the initial wave speed by the percentage increase:
Increase in wave speed = 20% of 150 m/s = 0.2 * 150 m/s = 30 m/s
Step 3: Determine the new wave speed.
The new wave speed will be the sum of the initial wave speed and the increase in wave speed:
New wave speed = Initial wave speed + Increase in wave speed = 150 m/s + 30 m/s = 180 m/s
Step 4: Calculate the initial tension.
The initial tension in the string is given as 120 N.
Step 5: Determine the increase in tension required.
To find the increase in tension required, we can use the following formula which relates tension, mass per unit length (μ), and wave speed (v):
Tension = μ * v^2
Since the wave speed is changing, we assume the mass per unit length remains constant. Thus, we can write:
Initial tension = μ * (Initial wave speed)^2
New tension = μ * (New wave speed)^2
Step 6: Calculate the new tension.
Using the formulas mentioned above, we can find the new tension in terms of the initial tension and the increase in wave speed:
New tension = Initial tension + Increase in tension
New tension = Initial tension + (New tension - Initial tension)
New tension = Initial tension + (μ * (New wave speed)^2 - μ * (Initial wave speed)^2)
Step 7: Substitute the known values and calculate the increase in tension.
Substituting the given values, the increase in tension required can be calculated using the equation from step 6.