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.


A string of length 5.0 m and mass 90 g is held under a tension of 1.0×10 N. A wave travels down the string that is modeled as 𝑦(𝑥,𝑡)=0.010(0.40𝑥1,170.12𝑡)msin, where 𝑥 is measured in meters and 𝑡 is measured in seconds. What is the power of the wave over one wavelength?


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 𝑃=𝐼𝑉. 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?

  • A1.72×10 kg/m
  • B1.37×10 kg/m
  • C3.00×10 kg/m
  • D2.00×10 kg/m
  • E2.55×10 kg/m


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?


A traveling wave on a string is modeled by the wave equation 𝑦(𝑥,𝑡)=4.50(6.30𝑥+85.0𝑡)sin, where 𝑥 is measured in meters and 𝑡 is measured in seconds. The string has a linear mass density 𝜇=0.0170/kgm. What is the average power transferred by the wave on the string?

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