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 of 90 g is held under a tension of 1 . 0 × 1 0 2 N. A wave travels down the string that is modeled as 𝑦 ( 𝑥 , 𝑡 ) = 0 . 0 1 0 ( 0 . 4 0 𝑥 1 1 7 0 . 1 2 𝑡 ) m s i n , where 𝑥 is measured in meters and 𝑡 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 𝑃 = 𝐼 𝑉 . Assume that the string vibrator is 9 0 . 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 1 . 7 2 × 1 0 4 kg/m
  • B 1 . 3 7 × 1 0 4 kg/m
  • C 2 . 5 5 × 1 0 4 kg/m
  • D 2 . 0 0 × 1 0 4 kg/m
  • E 3 . 0 0 × 1 0 4 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 𝑦 ( 𝑥 , 𝑡 ) = 4 . 5 0 ( 6 . 3 0 𝑥 + 8 5 . 0 𝑡 ) s i n , where 𝑥 is measured in meters and 𝑡 is measured in seconds. The string has a linear mass density 𝜇 = 0 . 0 1 7 0 / k g m . What is the average power transferred by the wave on the string?

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