Standing waves are wave patterns that stay in place, formed when two waves of the same frequency and amplitude travel in opposite directions and interfere.
The pattern looks frozen, with points that never move and others that vibrate the most.
Showing a random 20 of 50 problems.
Example 1
challenge
A closed-open pipe and an open-open pipe both have fundamental frequency 200 Hz. The closed-open pipe is how many times the length of the open-open pipe?
Example 2
medium
At a node of a standing wave, the displacement is always _____ and the pressure variation (for sound in a tube) is _____.
Example 3
easy
How many half-wavelengths fit on a fixed-fixed string in its 3rd mode (n=3)?
Example 4
medium
A string vibrates in its 3rd harmonic at 300 Hz. The wave speed is 200 m/s. Find the string length.
Example 5
medium
A guitar string of length 0.65 m has wave speed 400 m/s. Find the fundamental frequency.
Example 6
hard
A guitar string sounds A4 (440 Hz) as its fundamental. The player presses a fret so the vibrating length is 80% of the original. What is the new fundamental frequency?
Example 7
medium
A fixed-fixed string at n=2 has wavelength 0.5 m. Find the string length.n = 2, λ = 0.5 m. Find string length L.
Example 8
easy
Two waves travel in opposite directions with the same frequency and amplitude. The pattern they form is called a __________.
Example 9
challenge
A wire fixed at both ends (length 0.75 m) has wave speed 300 m/s. Find the frequency of its 3rd harmonic.
Example 10
medium
A string under tension T=80 N has linear density μ=0.005 kg/m, length 1.0 m. Find the fundamental frequency. (Use v=T/μ.)
Example 11
easy
What is an antinode in a standing wave?
Example 12
easy
A standing wave on a fixed-fixed string has fundamental wavelength λ1=2.0 m. What is the string length L?Fundamental wavelength λ₁ = 2.0 m. What is the string length L?
Example 13
medium
A fixed-fixed string of length 0.8 m supports a standing wave with 3 half-wavelengths (n=3). Find the wavelength.Find λ when L = 0.8 m and n = 3
Example 14
easy
In the fundamental mode of a fixed-fixed string, how many antinodes are there?
Example 15
medium
On a fixed-fixed string, the 2nd harmonic has frequency 180 Hz. What is the fundamental?
Example 16
challenge
Two waves y1=Asin(kx−ωt) and y2=Asin(kx+ωt) superpose. The resulting standing wave has the form 2Asin(kx)cos(ωt). At what positions x (smallest positive) is the first node, given k=π per meter?y₁ and y₂ superpose; find first node position (k = π rad/m)
Example 17
medium
A standing wave has nodes 0.4 m apart. What is the wavelength?Nodes are 0.4 m apart. Find the wavelength λ.
Example 18
easy
A standing wave on a string forms with n=1. Using L=n2λ, find λ if L=0.6 m.Find λ when L = 0.6 m and n = 1
Example 19
medium
A string 1.2 m long vibrates at 150 Hz with wavelength 0.6 m. (a) What mode is this? (b) What is the wave speed?
Example 20
easy
Are standing waves a new kind of wave or an interference pattern?