Questions: The speed of a transverse wave on a string is 170 m / s when the string tension is 120 N. To what value must the tension be changed to raise the wave speed to 180 m / s? Hints: v = sqrt(F/mu) and you are solving for mu first and in the second part, you are using mu to calculate F ? [mark all correct answers] a. 195 N b. 132 N c. 155 N d. 145 N e. 105 N f. 35 N

Solution Steps

The speed of a transverse wave on a string is given by the formula: \[ v = \sqrt{\frac{F}{\mu}} \]

Given:

• \( v = 170 \, \text{m/s} \)
• \( F = 120 \, \text{N} \)

We need to solve for \(\mu\): \[ 170 = \sqrt{\frac{120}{\mu}} \]

Square both sides to eliminate the square root: \[ 170^2 = \frac{120}{\mu} \] \[ 28900 = \frac{120}{\mu} \]

Rearrange to solve for \(\mu\): \[ \mu = \frac{120}{28900} \] \[ \mu = 0.004152 \, \text{kg/m} \]

Given the new wave speed:

• \( v' = 180 \, \text{m/s} \)

We use the same wave speed formula: \[ v' = \sqrt{\frac{F'}{\mu}} \]

Substitute the known values: \[ 180 = \sqrt{\frac{F'}{0.004152}} \]

Square both sides to eliminate the square root: \[ 180^2 = \frac{F'}{0.004152} \] \[ 32400 = \frac{F'}{0.004152} \]

Rearrange to solve for \(F'\): \[ F' = 32400 \times 0.004152 \] \[ F' = 134.9248 \, \text{N} \]

Final Answer