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A bullet is fired and moves at a speed of 1342 mph. Assume the speed of sound is v = 340.00 m/s . What is the angle of the shock wave produced?

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A speaker is placed at the opening of a long horizontal tube. The speaker oscillates at a frequency of f , creating a sound wave that moves down the tube. The wave moves through the tube at a speed of v = 340.00 m/s . The sound wave is modeled with the wave function s ( x , t ) = s max cos ( k x ω t + ϕ ) . At time t = 0.00 s , an air molecule at x = 2.3 m is at the maximum displacement of 6.34 nm. At the same time, another molecule at x = 2.7 m has a displacement of 2.30 nm. What is the wave function of the sound wave, that is, find the wave number, angular frequency, and the initial phase shift?

s 1 = 6.34 nm s 2 = 2.30 nm k x 1 + ϕ = 0 rad k x 2 + ϕ = 1.20 rad k ( x 2 x 1 ) = 1.20 rad k = 3.00 m −1 ω = 1019.62 s −1 s 1 = s max cos ( k x 1 ϕ ) ϕ = 5.66 rad s ( x , t ) = 6.30 nm cos ( 3.00 m −1 x 1019.62 s −1 t + 5.66 )

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An airplane moves at Mach 1.2 and produces a shock wave. (a) What is the speed of the plane in meters per second? (b) What is the angle that the shock wave moves?

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Additional problems

A 0.80-m-long tube is opened at both ends. The air temperature is 26 ° C . The air in the tube is oscillated using a speaker attached to a signal generator. What are the wavelengths and frequencies of first two modes of sound waves that resonate in the tube?

v s = 346.40 m/s ;
λ n = 2 n L f n = v s λ n λ 1 = 1.60 m f 1 = 216.50 Hz λ 2 = 0.80 m f 1 = 433.00 Hz

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A tube filled with water has a valve at the bottom to allow the water to flow out of the tube. As the water is emptied from the tube, the length L of the air column changes. A 1024-Hz tuning fork is placed at the opening of the tube. Water is removed from the tube until the n = 5 mode of a sound wave resonates. What is the length of the air column if the temperature of the air in the room is 18 ° C?

Picture shows a tuning fork placed above the opening of the tube filled with the water. Water is removed from the tube for the distance L.
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Consider the following figure. The length of the string between the string vibrator and the pulley is L = 1.00 m . The linear density of the string is μ = 0.006 kg/m . The string vibrator can oscillate at any frequency. The hanging mass is 2.00 kg. (a)What are the wavelength and frequency of n = 6 mode? (b) The string oscillates the air around the string. What is the wavelength of the sound if the speed of the sound is v s = 343.00 m/s ?

Picture shows a string vibrator connected to a frictionless pulley with a hanging mass of m. The distance of the string connecting the vibrator to the pulley is L.

a. λ 6 = 0.40 m v = 57.15 m s f 6 = 142.89 Hz ; b. λ s = 2.40 m

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Early Doppler shift experiments were conducted using a band playing music on a train. A trumpet player on a moving railroad flatcar plays a 320-Hz note. The sound waves heard by a stationary observer on a train platform hears a frequency of 350 Hz. What is the flatcar’s speed in mph? The temperature of the air is T C = 22 ° C .

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Two cars move toward one another, both sounding their horns ( f s = 800 Hz ) . Car A is moving at 65 mph and Car B is at 75 mph. What is the beat frequency heard by each driver? The air temperature is T C = 22.00 ° C .

v = 344.08 m s v A = 29.05 m s , v B = 33.52 m/s f A = 961.18 Hz, f B = 958.89 Hz f A , beat = 161.18 Hz, f B , beat = 158.89 Hz

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Student A runs after Student B. Student A carries a tuning fork ringing at 1024 Hz, and student B carries a tuning fork ringing at 1000 Hz. Student A is running at a speed of v A = 5.00 m/s and Student B is running at v B = 6.00 m/s . What is the beat frequency heard by each student? The speed of sound is v = 343.00 m/s .

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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