Ch 16: Traveling Waves
Back
Problem 15
When a guitar string plays the note 'A,' the string vibrates at 440 Hz. What is the period of the vibration?Problem 16
A friend of yours is loudly singing a single note at 400 Hz while racing toward you at 25.0 m/s on a day when the speed of sound is 340 m/s. a. What frequency do you hear?Problem 16
A physics professor demonstrates the Doppler effect by tying a 600 Hz sound generator to a 1.0-m-long rope and whirling it around her head in a horizontal circle at 100 rpm. What are the highest and lowest frequencies heard by a student in the classroom?Problem 16
A bat locates insects by emitting ultrasonic 'chirps' and then listening for echoes from the bugs. Suppose a bat chirp has a frequency of 25 kHz. How fast would the bat have to fly, and in what direction, for you to just barely be able to hear the chirp at 20 kHz?Problem 16
The wave speed on a string under tension is 200 m/s. What is the speed if the tension is halved?Problem 16
A string that is under 50.0 N of tension has linear density 5.0 g/m. A sinusoidal wave with amplitude 3.0 cm and wavelength 2.0 m travels along the string. What is the maximum speed of a particle on the string?Problem 16
String 1 in FIGURE P16.47 has linear density 2.0 g/m and string 2 has linear density . A student sends pulses in both directions by quickly pulling up on the knot, then releasing it. What should the string lengths L₁ and L₂ be if the pulses are to reach the ends of the strings simultaneously?
Problem 16
FIGURE P16.57 shows a snapshot graph of a wave traveling to the right along a string at 45 m/s. At this instant, what is the velocity of points 1, 2, and 3 on the string?
Problem 16
The string in FIGURE P16.59 has linear density μ. Find an expression in terms of M, μ, and θ for the speed of waves on the string.
Problem 16
FIGURE EX16.8 is a picture at t = 0 s of the particles in a medium as a longitudinal wave is passing through. The equilibrium spacing between the particles is 1.0 cm. Draw the snapshot graph D(x, t = 0 s) of this wave at t = 0 s.
Problem 16
What are the sound intensity levels for sound waves of intensity (a) 3.0 x 10⁻⁶ W/m²?Problem 16
Show that the displacement D(x,t) = cx² + dt², where c and d are constants, is a solution to the wave equation. Then find an expression in terms of c and d for the wave speed.Problem 16
A sound wave is described by D (y,t) = (0.0200 mm) ✕ sin [(8.96 rad/m)y + (3140 rad/s)t + π/4 rad], where y is in m and t is in s. b. Along which axis is the air oscillating?Problem 16
One cue your hearing system uses to localize a sound (i.e., to tell where a sound is coming from) is the slight difference in the arrival times of the sound at your ears. Your ears are spaced approximately 20 cm apart. Consider a sound source 5.0 m from the center of your head along a line 45° to your right. What is the difference in arrival times? Give your answer in microseconds. Hint: You are looking for the difference between two numbers that are nearly the same. What does this near equality imply about the necessary precision during intermediate stages of the calculation?
Problem 16
An avant-garde composer wants to use the Doppler effect in his new opera. As the soprano sings, he wants a large bat to fly toward her from the back of the stage. The bat will be outfitted with a microphone to pick up the singer's voice and a loudspeaker to rebroadcast the sound toward the audience. The composer wants the sound the audience hears from the bat to be, in musical terms, one half-step higher in frequency than the note they are hearing from the singer. Two notes a half-step apart have a frequency ratio of 2¹/² = 1.059. With what speed must the bat fly toward the singer?Problem 16
What is the speed of sound in air (a) on a cold winter day in Minnesota when the temperature is -25°F, and (b) on a hot summer day in Death Valley when the temperature is 125°F?Problem 16
Show that the displacement D(x,t) = ln(ax + bt), where a and b are constants, is a solution to the wave equation. Then find an expression in terms of a and b for the wave speed.Problem 17
Piano tuners tune pianos by listening to the beats between the harmonics of two different strings. When properly tuned, the note A should have a frequency of 440 Hz and the note E should be at 659 Hz. a.What is the frequency difference between the third harmonic of the A and the second harmonic of the E?Problem 17
A violinist places her finger so that the vibrating section of a 1.0 g/m string has a length of 30 cm, then she draws her bow across it. A listener nearby in a 20°C room hears a note with a wavelength of 40 cm. What is the tension in the string?Problem 17
INT One end of a 75-cm-long, 2.5 g guitar string is attached to a spring. The other end is pulled, which stretches the spring. The guitar string's second harmonic occurs at 550 Hz when the spring has been stretched by 5.0 cm. What is the value of the spring constant?Problem 17
A string under tension has a fundamental frequency of 220 Hz. What is the fundamental frequency if the tension is doubled?Problem 17
FIGURE EX17.6 shows a standing wave oscillating at 100 Hz on a string. What is the wave speed?
Problem 17
a. What are the three longest wavelengths for standing waves on a 60 cm long string that is fixed at both ends?Problem 17
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.Problem 17
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.Problem 17
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.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?Problem 17
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?Problem 17
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?Problem 17
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?
