Textbook Question
Standing waves on a 1.0-m-long string that is fixed at both ends are seen at successive frequencies of 36 Hz and 48 Hz.
b. Draw the standing-wave pattern when the string oscillates at 48 Hz.
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Ch 16: Traveling Waves
Chapter 16, Problem 17
A carbon dioxide laser is an infrared laser. A CO2 laser with a cavity length of 53.00 cm oscillates in the m=100,000 mode. What are the wavelength and frequency of the laser beam?
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Laser Oscillation Modes
In laser physics, oscillation modes refer to the specific standing wave patterns that can form within the laser cavity. Each mode is characterized by a quantum number, which indicates the number of wavelengths fitting into the cavity length. The m=100,000 mode signifies a high-frequency oscillation, which is crucial for determining the laser's wavelength and frequency.
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Wavelength and Frequency Relationship
The wavelength and frequency of a wave are inversely related through the equation c = λf, where c is the speed of light, λ is the wavelength, and f is the frequency. This relationship means that as the wavelength increases, the frequency decreases, and vice versa. Understanding this relationship is essential for calculating the wavelength and frequency of the CO2 laser beam.
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Cavity Length and Wavelength
The cavity length of a laser influences the wavelengths of light that can resonate within it. The fundamental wavelength can be determined using the formula λ = 2L/m, where L is the cavity length and m is the mode number. For the CO2 laser with a cavity length of 53.00 cm and m=100,000, this formula allows us to calculate the specific wavelength of the emitted laser light.
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Related Practice
Textbook Question
The two highest-pitch strings on a violin are tuned to 440 Hz (the A string) and 659 Hz (the E string). What is the ratio of the mass of the A string to that of the E string? Violin strings are all the same length and under essentially the same tension.
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Textbook Question
BIO Ultrasound has many medical applications, one of which is to monitor fetal heartbeats by reflecting ultrasound off a fetus in the womb.
a. Consider an object moving at speed vo toward an at-rest source that is emitting sound waves of frequency f0 . Show that the reflected wave (i.e., the echo) that returns to the source has a Doppler-shifted frequency
fecho = (v+v0 / v-vo) fo
where v is the speed of sound in the medium.
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Textbook Question
When mass M is tied to the bottom end of a long, thin wire suspended from the ceiling, the wire's second-harmonic frequency is 200 Hz. Adding an additional 1.0 kg to the hanging mass increases the second-harmonic frequency to 245 Hz. What is M?
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Textbook Question
Two loudspeakers emit sound waves along the x-axis. The sound has maximum intensity when the speakers are 20 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 60 cm.
a. What is the wavelength of the sound?
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Textbook Question
Two loudspeakers in a 20°C room emit 686 Hz sound waves along the x-axis.
b. If the speakers are out of phase, what is the smallest distance between the speakers for which the interference of the sound waves is maximum constructive?
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