Exercise \(\PageIndex{1}\): Find the frequency of the wave
Find the frequency of the wave shown in the animation (position is given in centimeters and time is given in seconds). Restart.
Exercise \(\PageIndex{2}\): Find the velocity of the wave
Find the velocity of the wave shown in the animation (position is given in centimeters and time is given in seconds). Restart.
Exercise \(\PageIndex{3}\): Determine the tension in the string
The animation shows disturbances on two identical strings (position is given in centimeters and time is given in seconds). What is the tension in the second string if the tension in the first string is \(500\text{ N}\)? Restart.
Exercise \(\PageIndex{4}\): Properties of the superposition of two waves
The animation shows disturbances on two identical strings (position is given in centimeters and time is given in seconds). Restart.
At \(t = 2.5\) seconds, which of the following, if any, statement(s) is (are) true regarding the superposition of the two waves?
- Their sum adds up to zero.
- Their sum adds up to twice that of the original waves.
- Their sum is as if only one of the original waves is there.
- Their sum has a large peak, a depression, and then another large peak.
Exercise \(\PageIndex{5}\): Properties of the superposition of two waves
The animation shows disturbances on two identical strings (position is given in centimeters and time is given in seconds). Restart.
At \(t = 2.0\text{ s}\), which of the following, if any, statement(s) is (are) true regarding the superposition of the two waves?
- Their sum adds up to zero.
- Their sum adds up to twice that of the original waves.
- Their sum is as if only one of the original waves is there.
- Their sum has a large peak, a depression, and then another large peak.
Exercise \(\PageIndex{6}\): Properties of the superposition of two waves
The animation shows how two waves can add together to produce a standing wave on a string (position is given in centimeters and time is given in seconds). The third panel represents the string. The waves in the first two panels have been superimposed to produce the wave in the third panel. Restart.
Which of the following, if any, statement(s) is(are) true?
- Waves never pass through the point \(x = 0\text{ cm}\) on the string since this point never moves.
- The string is perfectly straight when the maxima in the first two panels overlap.
- There is an instant in time when the string does not move.
- The string is moving fastest when the maxima in the first two panels overlap.
Exercise \(\PageIndex{7}\): With what speed do waves propagate on a string?
The animation shows a standing wave on a string (position is given in centimeters and time is given in seconds). With what speed do waves propagate on this string? Restart.
Exercise \(\PageIndex{8}\): Determine the mass of the string
The animation shows a standing wave on a string (position is given in meters and time is given in seconds). If the tension in the string is \(4\text{ N}\), determine the mass of the string. Restart.
Exercise \(\PageIndex{9}\): Determine the properties of the wave
Shown in black is a wave (position is given in meters). Three sliders are given that change certain properties of the wave. Restart.
- Which slider changes which property of the wave?
- Use the sliders to identify the wave parameters for this wave function (shown in red).
Problem authored by Morten Brydensholt, Wolfgang Christian, and Mario Belloni.
Script authored by Morten Brydensholt, Wolfgang Christian, and Mario Belloni.
Exercise \(\PageIndex{10}\): Determine the properties of the traveling wave
- Measure the frequency, wavelength, and period of the wave (position is given in centimeters and time is given in seconds)
- Verify that the speed of the wave crest is wavelength times frequency.
- Write down a formula for the wave as a function of both distance and time. That is, write a formula for \(y(x, t)\).
Restart.
Exercise \(\PageIndex{11}\): Determine the properties of the standing wave
The animation shows a standing wave on a string (position is given in meters and time is given in seconds). Restart.
- What is the speed of waves traveling on this string?
- Assume you are standing at the point \(x = 2\text{ m}\). Sketch the height of the wave at this point as a function of time.
- Write an equation for the height of the wave as a function of time at the points \(x = 0\text{ m}\) and \(x = 2\text{ m}\).
- Write down a formula for the wave as a function of both distance and time. That is, write a formula for \(y(x, t)\).
Exercise \(\PageIndex{12}\): Determine the properties of the standing wave
Two traveling waves (the top two panels) are depicted on a string (position is given in meters and time is given in seconds). They are traveling in opposite directions and add to a standing wave as depicted in the bottom panel. Restart.
- What are the wavelength, frequency, and velocity of the initial two waves?
- What are the wavelength, frequency, and velocity of the resulting standing wave?
Exercise \(\PageIndex{13}\): Determine the wave function
Shown in black is a traveling wave (position is given in centimeters and time is given in seconds). Measure the relevant properties of this wave and determine the wave function of the wave. Restart.
Exercise \(\PageIndex{14}\): Determine the properties of a standing wave on a taut string
The animation shows a portion of a standing wave on a taut string (position is given in centimeters and time is given in seconds). Restart.
- What is the speed of a wave traveling to the right on this string?
- Write an equation for the height of the string as a function of both position and time. That is, write a formula for \(y(x, t)\).
Exercise \(\PageIndex{15}\): Determine the properties of a standing wave on a taut string
The animation shows a portion of a standing wave on a taut string (position is given in centimeters and time is given in seconds). Restart.
- Measure the frequency, wavelength, and period of the wave in the animation.
- Write a formula for the position as a function of time for a small section of string located at \(x = 0\text{ cm}\) and a formula for \(x = 2\text{ cm}\).
- Write a formula for the velocity as a function of time for a small section of string located at \(x = 0\text{ cm}\) and a formula for \(x = 2\text{ cm}\).
- Sketch the velocity of the string as a function of \(x\) at \(t = 0\text{ cm}\). That is, show how each small section of string is moving at \(t = 0\text{ s}\).
Exercise \(\PageIndex{16}\): Consider a traveling sinusoidal wave on a string
The animation marks sections of a taut string with small circles. You can change the number of small circles (the wave markers) by dragging the slider. Consider a traveling sinusoidal wave on this string. Restart
- Describe the motion of a small section of this string. Does a section of string ever move to the right or left?
- Write an equation, \(f(t)\), that describes the motion of a small section of the string shown.
- Compare the motion of two different small sections of string. What is the same and what is different?
- If the wave function is not shown, how many markers are needed to clearly discern the sinusoidal nature of the wave function? What mistake are you likely to make if you use too few markers?
- Write an equation, \(f(x, t)\), that describes this wave.
Exercise \(\PageIndex{17}\): Sketch the displacement of the point \(x=0\text{ cm}\)
- Sketch the displacement of each wave at the point \(x = 0\text{ cm}\) as a function of time (position is given in centimeters and time is given in seconds).
- How do your sketches change if you measure the waves at \(x = 2\text{ cm}\)?
Restart.
Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.
