Chapter 16

A college student is at a concert and really wants to hear the music, so she sits between two in-phase loudspeakers, which point toward each other and are \(50.0 \mathrm{~m}\) apart. The speakers emit sound at a frequency of \(490 .\) Hz. At the midpoint between the speakers, there will be constructive interference, and the music will be at its loudest. At what distance closest to the midpoint could she also sit to experience the loudest sound?

A string of a violin produces 2 beats per second when sounded along with a standard fork of frequency \(400 . \mathrm{Hz}\). The beat frequency increases when the string is tightened. a) What was the frequency of the violin at first? b) What should be done to tune the violin?

You are playing a note that has a fundamental frequency of \(400 .\) Hz on a guitar string of length \(50.0 \mathrm{~cm}\). At the same time, your friend plays a fundamental note on an open organ pipe, and 4 beats per seconds are heard. The mass per unit length of the string is \(2.00 \mathrm{~g} / \mathrm{m}\). Assume the velocity of sound is \(343 \mathrm{~m} / \mathrm{s}\). a) What are the possible frequencies of the open organ pipe? b) When the guitar string is tightened, the beat frequency decreases. Find the original tension in the string. c) What is the length of the organ pipe?

Two 100.0-W speakers, A and B, are separated by a distance \(D=3.6 \mathrm{~m} .\) The speakers emit in-phase sound waves at a frequency \(f=10,000.0 \mathrm{~Hz}\). Point \(P_{1}\) is located at \(x_{1}=4.50 \mathrm{~m}\) and \(y_{1}=0 \mathrm{~m} ;\) point \(P_{2}\) is located at \(x_{2}=4.50 \mathrm{~m}\) and \(y_{2}=-\Delta y .\) Neglecting speaker \(\mathrm{B}\), what is the intensity, \(I_{\mathrm{A} 1}\) (in \(\mathrm{W} / \mathrm{m}^{2}\) ), of the sound at point \(P_{1}\) due to speaker \(\mathrm{A}\) ? Assume that the sound from the speaker is emitted uniformly in all directions. What is this intensity in terms of decibels (sound level, \(\beta_{\mathrm{A} 1}\) )? When both speakers are turned on, there is a maximum in their combined intensities at \(P_{1} .\) As one moves toward \(P_{2},\) this intensity reaches a single minimum and then becomes maximized again at \(P_{2}\). How far is \(P_{2}\) from \(P_{1},\) that is, what is \(\Delta y ?\) You may assume that \(L \gg \Delta y\) and that \(D \gg \Delta y\), which will allow you to simplify the algebra by using \(\sqrt{a \pm b} \approx a^{1 / 2} \pm \frac{b}{2 a^{1 / 2}}\) when \(a \gg b\).

A policeman with a very good ear and a good understanding of the Doppler effect stands on the shoulder of a freeway assisting a crew in a 40 -mph work zone. He notices a car approaching that is honking its horn. As the car gets closer, the policeman hears the sound of the horn as a distinct \(\mathrm{B} 4\) tone \((494 \mathrm{~Hz}) .\) The instant the car passes by, he hears the sound as a distinct \(\mathrm{A} 4\) tone \((440 \mathrm{~Hz}) .\) He immediately jumps on his motorcycle, stops the car, and gives the motorist a speeding ticket. Explain his reasoning.

A meteorite hits the surface of the ocean at a speed of \(8800 \mathrm{~m} / \mathrm{s}\). What are the shock wave angles it produces (a) in the air just before hitting the ocean surface, and (b) in the ocean just after entering? Assume the speed of sound in air and in water is \(343 \mathrm{~m} / \mathrm{s}\) and \(1560 \mathrm{~m} / \mathrm{s}\), respectively.

A train whistle emits a sound at a frequency \(f=3000 .\) Hz when stationary. You are standing near the tracks when the train goes by at a speed of \(v=30.0 \mathrm{~m} / \mathrm{s}\). What is the magnitude of the change in the frequency \((|\Delta f|)\) of the whistle as the train passes? (Assume that the speed of sound is \(v=343 \mathrm{~m} / \mathrm{s}\).)

You are driving along a highway at \(30.0 \mathrm{~m} / \mathrm{s}\) when you hear a siren. You look in the rear-view mirror and see a police car approaching you from behind with a constant speed. The frequency of the siren that you hear is \(1300 \mathrm{~Hz}\). Right after the police car passes you, the frequency of the siren that you hear is \(1280 \mathrm{~Hz}\). a) How fast was the police car moving? b) You are so nervous after the police car passes you that you pull off the road and stop. Then you hear another siren, this time from an ambulance approaching from behind. The frequency of its siren that you hear is \(1400 \mathrm{~Hz}\). Once it passes, the frequency is \(1200 \mathrm{~Hz}\). What is the actual frequency of the ambulance's siren?

A bat flying toward a wall at a speed of \(7.0 \mathrm{~m} / \mathrm{s}\) emits an ultrasound wave with a frequency of \(30.0 \mathrm{kHz}\). What frequency does the reflected wave have when it reaches the flying bat?

You are traveling in a car toward a hill at a speed of \(40.0 \mathrm{mph} .\) The car's horn emits sound waves of frequency \(250 \mathrm{~Hz},\) which move with a speed of \(340 \mathrm{~m} / \mathrm{s}\) a) Determine the frequency with which the waves strike the hill. b) What is the frequency of the reflected sound waves you hear? c) What is the beat frequency produced by the direct and the reflected sounds at your ears?