The width of a particular microwave oven is exactly right to support a standing-wave mode. Measurements of the temperature across the oven show that there are cold spots at each edge of the oven and at three spots in between. The wavelength of the microwaves is 12 cm. How wide is the oven?

What are the frequencies associated with these two wavelengths?

For a standing wave on a rope, the distance between two adjacent antinodes is (a) 1/4 wavelength, (b) 1/2 wavelength, (c) one wavelength, (d) two wavelengths.

The microwaves in a certain microwave oven have a wavelength of $12.2 \mathrm{~cm}$.

What is the frequency of these microwaves?

A string is vibrating back and forth. The tension in the string is decreased by a factor of four, with the frequency and the length of the string remaining the same. Draw the new standing wave pattern that develops on the string. Give your reasoning.

As we discussed earlier shows a standing wave on a string. Point $\mathrm{A}$ on the string is shown at time $t=0$. In terms of the wave's period $T$, what are the earliest times after $t=0$ that points B, C, and D reach the positions shown?

A string that is $30.0 \mathrm{~cm}$ long and has a mass per unit length of $9.00 \times 10^{-3} \mathrm{~kg} / \mathrm{m}$ is stretched to a tension of $20.0 \mathrm{~N}$. Find
(b) the next three frequencies that could cause standing-wave patterns on the string.

The period of a pulsating variable star may be estimated by considering the star to be executing radial longitudinal pulsations in the fundamental standing wave mode; that is, the star's radius varies periodically with time, with a displacement antinode at the star's surface. Typical white dwarf stars are composed of material with a bulk modulus of 1.33 * 10 raised to (22) Pa and a density of 10 raised to 10 kg per meter cube. They have radii equal to 9.0 * 10 raised to (-3) solar radius. What is the approximate pulsation period of a white dwarf?

An object of mass m hangs in equilibrium from a string with a total length L and a linear mass density $\mu$. The string is wrapped around two light, frictionless pulleys that are separated by a distance d. (a) Determine the tension in the string. (b) At what frequency must the string between the pulleys vibrate to form the standing-wave pattern?

A clothesline is stretched $9 \mathrm{~m}$ between two trees. Clothes hang on the line as below. When a particular standing wave is produced in the line by shaking the line, the clothes remain stationary.

a) What is the term for the positions occupied by the clothes?

b) What is the wavelength of this standing wave?

c) What additional wavelengths could exist in the line that the clothes remain stationary?

An air-filled cavity for producing electromagnetic standing waves has two parallel, highly conducting walls separated by a distance L. One standing-wave pattern in the cavity produces nodal planes of the electric field with a spacing of 1.50 cm. The next-higher-frequency standing wave in the cavity produces nodal planes with a spacing of 1.25 cm. What is the distance L between the walls of the cavity?

Verify by substitution that the standing wave general solution, (6-67), satisfies the time-independent Schroendinger equation, (6-62), for the infinite square well potential in the region inside the well.

A 3.00-m-long string, fixed at both ends, has a mass of $6.00 \mathrm{~g}$. If you want to set up a standing wave in this string having a frequency of $300 . \mathrm{Hz}$ and three antinodes, what tension should you put the string under?

A 2.0-m-long string carries a standing wave as in the figure at right. Extend the pattern and the formulas shown in as we discussed earlier to determine the mode number and the wavelength of this particular standing-wave mode.
A. $m=6, \lambda=0.67 \mathrm{~m}$
B. $m=6, \lambda=0.80 \mathrm{~m}$
C. $m=5, \lambda=0.80 \mathrm{~m}$
D. $m=5, \lambda=1.0 \mathrm{~m}$
E. $m=4, \lambda=0.80 \mathrm{~m}$
F. $m=4, \lambda=1.0 \mathrm{~m}$