Physics Homework Chapter 14

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1. Earthquakes at fault lines in Earth's crust create seismic waves, which are longitudinal (P-waves) or transverse (S-waves). The P-waves have a speed of about 5 km/s. Estimate the average bulk modulus of Earth's crust given that the density of rock is about 2,700 kg/m³.
_____ Pa






2. On a hot summer day, the temperature of air in Arizona reaches 101°F. What is the speed of sound in air at this temperature? (Enter your answer to four significant figures. The speed of sound at 0°C is 331 m/s. use the conversion 0°C = 273 K as necessary.)
_____ m/s






3. A group of hikers hears an echo 2.10 s after shouting. how far away is the mountain that reflected the sound wave? (Assume the speed of sound is 340.6 m/s.)
_____ m







4. The range of human hearing extends from approximately 20 Hz to 20,000 Hz. Find the wavelengths of these extremes at a temperature of 11°C.
20 Hz        _____ m
20,000 Hz _____ m







5. When at res, two trains have sirens that emit a frequency of 300 Hz. The trains travel toward one another and toward an observer stationed between them. One of the trains moves at 32.5 m/s, and the observer hears a beat frequency of 2.9 beats per second. What is the speed of the second train, which travels faster than 32.5 m/s?
_____ m/s






6. Two trains on separate tracks move toward each other. Train 1 has a speed of 137 km/h; train 2 a speed of 77.0 km/h. Train 2 blows its horn, emitting a frequency of 500 Hz. What is the frequency heard by the engineer on train 1?
_____ Hz






7. At rest, a car's horn sounds the note A (440 Hz). The horn is sounded while the car is moving down the street. A bicyclist moving in the same direction with one-third the car's speed hears a frequency of 413 Hz.

a) Is the cyclist ahead of or behind the car?
_____

b) What is the speed of the car?
_____ m/s








8. An alert physics student stands beside the tracks as a train rolls slowly past. He notes that the frequency of the train whistle is 490 hz when the train is approaching him and 471 Hz when the train is receding form him. Using these frequencies, he calculates the speed of the train. What value does he find?
_____ m/s






9. A steel wire in a piano has a length of 0.7000 m and a mass of 3.900 x 10^-3 kg. To what tension must this wire be stretched so that the fundamental vibration corresponds to middle C (ƒ_c = 261.6 Hz on the chromatic musical scale)?
_____ N






10. A stretched string of length L is observed to vibrate in six equal segments when driven by a 637-Hz oscillator. What oscillator frequency will set up a standing wave so that the string vibrates in three segments?
_____ Hz






11. A steel wire with mass 27 g and length 1.15 m is strung on a bass so that the distance from the nut to the bridge is 1.10 m.

a) Compute the linear density of the string.
_____ kg/m

b) What velocity wave on the string will produce the desired fundamental frequency of the E₁ string, 45.23 Hz?
_____ m/s

c) Calculate the tension required to obtain the proper frequency.
_____ N

d) Calculate the wavelength of the string's vibration.
_____ m

e) What is the wavelength of the sound produced in air? (Assume the speed of sound in air is 343 m/s.)
_____ m






12. The windpipe of a typical whooping crane is about 5.1 ft long. What is the lowest resonant frequency of this pipe, assuming that it is closed at one end? Assume a temperature of 35°C.
_____ Hz






13. The human ear canal is about 2.4 cm long. If it is regarded as a tube open at one end and closed at the eardrum, what is the fundamental frequency around which we would expect hearing to be most sensitive?
_____ kHz






14. A pipe open at both ends has a fundamental frequency of 320 Hz when the temperature is 0°C.
a) What is the length of the pipe?
_____ m

b) What is the fundamental frequency at a temperature of 30°C?
_____ Hz






15. Two train whistles have identical frequencies of 1.47 x 10² Hz. When one train is at rest in the station and the other is moving nearby, a commuter standing on the station platform hears beats with a frequency of 8.00 beats/s when the whistles operate together. What are the two possible speeds that the moving train can have?
_____ m/s moving towards the station
_____ m/s moving away from the station