#### Sound and Waves

A sinusoidal transverse wave is traveling along a string in the negative direction of an x axis. The figure below shows a plot of the displacement as a function of position at time t= 0. The x axis is marked in increments of 10 cm and the y axis is marked in increments of 2.5 cm. The string tension is 3.1 N, and its linear density is 32 g/m. (a) Find the amplitude. (b) Find the wavelength. (c) Find the wave speed. (d) Find the period of the wave. (e) Find the maximum speed of a particle in the string. (f) Complete the equation describing the traveling wave, in which x and y are in meters, angle in radians, and tis in seconds.

A tube 1.32 m long is closed at one end. A stretched wire is placed near the open end. The wire is 0.370 m long and has a mass of 9.90 g. It is fixed at both ends and oscillates in its fundamental mode. By resonance, it sets the air column in the tube into oscillation at that column's fundamental frequency. (Use 343 m/s for the speed of sound in air.) (a) Find that frequency. (b) Find the tension in the wire.

A siren emitting a sound of frequency 1060 Hz moves away from you toward the face of a cliff at a speed of 13 m/s. Take the speed of sound in air as 330 m/s. (a) What is the frequency of the sound you hear coming directly from the siren? (Give your answer to at least one decimal place.) (b) What is the frequency of the sound you hear reflected off the cliff? (Give your answer to at least one decimal place.) (c) What is the beat frequency between the two sounds? Is it perceptible (less than 20 Hz)?

A girl is sitting near the open window of a train that is moving at a velocity of 20.00 m/s to the east. The girl's uncle stands near the tracks and watches the train move away. The locomotive whistle emits sound at frequency 560.0 Hz. The air is still. (Use 343.0 m/s for the speed of sound in air for all parts of this question. (a) What frequency does the uncle hear? (b) What frequency does the girl hear? (c) A wind begins to blow from the east at 20.00 m/s. What frequency does the uncle now hear? (d) What frequency does the girl now hear?

A state trooper chases a speeder along a straight stretch of road; both vehicles move at 164 km/h. The siren on the trooper's vehicle produces sound at a frequency of 575 Hz. What is the Doppler shift in the frequency heard by the speeder? (Assume the speed of sound in the air is 343 m/s.)

An ambulance with a siren emitting a whine at 1500 Hz overtakes and passes a cyclist pedaling a bike at 2.44 m/s. After being passed, the cyclist hears a frequency of 1490 Hz. How fast is the ambulance moving? (Use 343 m/s for the speed of sound in air.)

A point source emits 71.0 W of sound isotropically. A small microphone intercepts the sound in an area of 0.650 cm², 150 m from the source. (a) Calculate the sound intensity there. (b) Calculate the power intercepted by the microphone.

In the figure, two speakers separated by distance d = 1.90 m are in phase. Assume the amplitudes of the sound waves from the speakers are approximately the same at the listener's ear at distance d₂ = 3.95 m directly in front of one speaker. Consider the full audible range for normal hearing, 20 Hz to 20 kHz and use 343 m/s for the speed of sound in air. (a) What is the lowest frequency that gives minimum signal (destructive interference) at the listener's ear? (b) What is the second lowest frequency that gives minimum signal? (c) What is the third lowest frequency that gives minimum signal? (d) What is the lowest frequency that gives maximum signal (constructive interference) at the listener's ear? (e) What is the second lowest frequency that gives maximum signal? (f) What is the third lowest frequency that gives maximum signal?

A 5.0 W point source emits sound waves isotropically. Assuming the energy of the waves is conserved, find the following. (a) What is the intensity 1.0 m from the source? (b) What is the intensity 3.0 m from the source?

Two loudspeakers are located 3.80 m apart on an outdoor stage. A listener is 18.4 m from one and 19.1 m from the other. During the sound check, a signal generator drives the two speakers in phase with the same amplitude and frequency. The transmitted frequency is swept through the audible range (20 Hz-20 kHz). The speed of sound in the air is 343 m/s. What are the three lowest frequencies that give minimum signal (destructive interference) at the listener's location?