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 necessary to increase the wave speed by 20%, you can follow these steps:
Step 1: Determine the initial wave speed.
Given that the initial wave speed is 150 m/s, you can assign this value to the variable "V1."
V1 = 150 m/s
Step 2: Calculate the new wave speed after the 20% increase.
To find the new wave speed, you need to increase the initial wave speed by 20% and assign it to the variable "V2."
V2 = V1 + (20% of V1)
= V1 + (0.20 * V1)
= V1 * (1 + 0.20)
= V1 * 1.20
Step 3: Calculate the initial tension (T1) using the initial wave speed.
The wave speed on a string is related to tension (T) and linear mass density (µ) by the equation: V = √(T/µ).
We have the wave speed (V1) and we can assume the linear mass density (µ) remains constant. Rearranging the formula gives: T1 = V1^2 * µ.
Step 4: Calculate the new tension (T2) using the new wave speed.
Similarly, using the new wave speed (V2), we can calculate the new tension (T2): T2 = V2^2 * µ.
Step 5: Determine the percentage increase in tension.
The percentage increase in tension can be calculated as follows: % increase = ((T2 - T1) / T1) * 100%.
Now that we have established the necessary steps, let's plug in the values and compute the percentage increase:
T1 = V1^2 * µ
T2 = V2^2 * µ
% increase = ((T2 - T1) / T1) * 100%
Keep in mind that you will need to know the linear mass density (µ) to complete the calculation.