Lesson Worksheet: Resonance of Strings Physics

In this worksheet, we will practice determining the resonant oscillation frequency of a taut string and describing its harmonic oscillation modes.

Q1:

The diagram shows the standing waves that are produced by a string fixed at one end when the free end is oscillated at either of two different frequencies. The string is 2.5 m long and the speed of the traveling waves along the string is 7.5 m/s.

What is the frequency of the oscillation that produces the standing wave shown in red? Answer to one decimal place.

What is the frequency of the oscillation that produces the standing wave shown in blue? Answer to one decimal place.

Q2:

A string is held under tension at its fixed end, and its free end is oscillated. The string is 3.5 m long and has a mass of 0.12 kg. The fixed end of the string is held with a tension of 125 N. Find the lowest oscillation frequency at which the string produces a standing wave. Give your answer to the nearest hertz.

Q3:

A string is held under tension at its fixed end, and its free end is oscillated. The string is 2.5 m long and has a mass of 0.085 kg. The lowest oscillation frequency at which the string produces a standing wave is 12 Hz. Find the tension holding the fixed end of the string. Answer to the nearest newton.

Q4:

A string is held under tension at its fixed end and its free end is oscillated. If the string is replaced by a longer string that has the same mass, how does the lowest frequency at which standing waves will be produced change?

  • AThe frequency will increase.
  • BThe frequency will decrease.
  • CThe frequency will not change.

Q5:

A 4.5 m long string is held under tension at its fixed end, and its free end is oscillated at a frequency of 15 Hz, causing a standing wave to be generated. The fixed end of the string is held with a tension of 175 N. Find the mass of the string. Answer to the nearest gram.

Q6:

A string is held under tension at its fixed end, and its free end is oscillated. If the string is replaced by a string with a greater mass that has the same length, how does the lowest frequency at which standing waves will be produced change?

  • AThe frequency will increase.
  • BThe frequency will decrease.
  • CThe frequency will not change.

Q7:

A string is held under tension at its fixed end and its free end is oscillated. If the string is placed under greater tension, how does the lowest frequency at which standing waves will be produced change?

  • AThe frequency will increase.
  • BThe frequency will decrease.
  • CThe frequency will not change.

Q8:

A string is held under tension at its fixed end, and its free end is oscillated at a frequency of 3.6 Hz, causing a standing wave to be generated. The fixed end of the string is held with a tension in newtons equal to the mass of the string in kilograms. Find the length of the string. Answer to the nearest millimeter.

Q9:

The diagram shows five instants, separated by equal intervals, of the change in displacement of waves on a string with distance along the string from its free end. A traveling wave, represented by the green line, propagates from the free end of the string along the 𝑥-direction to a point 𝑥, where it reflects at an instant 𝑡.

How many wavelengths of the traveling wave is the distance from the free end of the string to 𝑥?

How many of its wavelengths does the traveling wave move through during the time interval between instants?

  • A0.125 wavelengths
  • B0.5 wavelengths
  • C1 wavelength
  • D0.25 wavelengths
  • E2 wavelengths

Q10:

The diagram shows five instants separated by equal intervals of the change in displacement of waves on a string with distance along the string from its free end. A traveling wave represented by the green line propagates from the free end of the string along the 𝑥-direction to a point 𝑥, where it reflects at the instant 𝑡.

What is the ratio of the wavelength of the stationary wave to the wavelength of the wave that arrives at 𝑥 at 𝑡?

What is the ratio of the amplitude of the stationary wave to the amplitude of the wave that arrives at 𝑥 at 𝑡?

This lesson includes 2 additional questions and 20 additional question variations for subscribers.

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