# Worksheet: Standing Waves

In this worksheet, we will practice describing the structures of standing waves that can form by resonance with objects of different lengths .

**Q1: **

A pipe that is open at both ends is 2.4 m long. What is the wavelength of a sound wave that has a frequency equal to the pipe’s fundamental frequency?

**Q2: **

A pipe is 75 cm long. Initially, one end of the pipe is closed, and a sound wave resonates in the pipe at the pipe’s fundamental frequency. The closed end of the pipe is then opened, and a new sound wave resonates at the open pipe’s fundamental frequency. What is the difference between the wavelengths of the two sound waves?

**Q3: **

A pipe that is closed at one end has a fundamental frequency of 48 Hz. The speed of sound in the air inside the pipe is 343 m/s. Find the length of the pipe. Give your answer to two significant figures.

**Q4: **

A pipe that is closed at one end is 0.35 m long. What is the wavelength of a sound wave that has a frequency equal to the pipe’s fundamental frequency?

**Q5: **

A pipe closed at one end is 0.125 m long. The fundamental frequency of the pipe is 666 Hz. What is the speed of sound in the air inside the pipe?

**Q6: **

Two traveling sound waves with different frequencies both resonate in a pipe that is 0.30 m long, which is open at both sides. The sound wave of longer wavelength has a wavelength equal to the length of the pipe. The other sound wave has a frequency that is one harmonic above the resonant frequency produced by the sound wave of longer wavelength. What is the difference between the wavelengths of the two traveling sound waves?

**Q7: **

A pipe is closed at one end. The wavelength of a sound wave that has a frequency equal to the fundamental frequency of the pipe is 1.4 m. Sound waves are generated at the pipe’s open end. The sound waves are initially at a frequency equal to the fundamental frequency of the pipe, and then the sound waves gradually change in wavelength. As the wavelength changes, the pipe resonates with the sound waves three times after they change from the fundamental frequency of the pipe. What is the wavelength of the sound waves when resonance occurs for the third time?

**Q8: **

Each of the following diagrams shows a wave on a string that has one end attached to a wall. The free end is oscillated, and a standing wave is formed on the string while the oscillations continue. In each diagram, the wave traveling along the string from its free end to its fixed end is shown at an instant . Which of the diagrams correctly represents the relationship at the instant between the wave traveling along the string from its free end to its fixed end and the wave traveling along the string from its fixed end to its free end?

- A
- B
- C
- D