Worksheet: Energy and Power of Waves on a String

In this worksheet, we will practice calculating the average power transmitted by mechanical waves on a taut string.

Q1:

A string of length 5.0 m and mass 90 g is held under a tension of N. A wave travels down the string that is modeled as , where is measured in meters and is measured in seconds. What is the power of the wave over one wavelength?

Q2:

A wave on a string is driven by a string vibrator, which oscillates at a frequency of 100.00 Hz and an amplitude of 1.00 cm. The string vibrator operates at a voltage of 12.00 V and a current of 0.200 A. The power consumed by the string vibrator is . Assume that the string vibrator is 90.0% efficient at converting electrical energy into the energy associated with the vibrations of the string. The string is 3.00 m long and is under a tension of 60.00 N. What is the linear mass density of the string?

• A kg/m
• B kg/m
• C kg/m
• D kg/m
• E kg/m

Q3:

A transverse wave on a string has a wavelength of 5.0 m, a period of 0.020 s, and an amplitude of 1.5 cm. The average power transferred by the wave is 5.0 W. What is the tension in the string?

Q4:

A traveling wave on a string is modeled by the wave equation , where is measured in meters and is measured in seconds. The string has a linear mass density . What is the average power transferred by the wave on the string?