COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 13, Problem 53QAP
To determine
The speeds of sounds in glycerin.
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Chapter 13 Solutions
COLLEGE PHYSICS
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- An ultrasonic tape measure uses frequencies above 20 MHz to determine dimensions of structures such as buildings. It does so by emitting a pulse of ultrasound into air and then measuring the time interval for an echo to return from a reflecting surface whose distance away is to be measured. The distance is displayed as a digital readout. For a tape measure that emits a pulse of ultrasound with a frequency of 22.0 MHz., (a) what is the distance to an object from which the echo pulse returns after 24.0 ms when the air temperature is 26C? (b) What should be the duration of the emitted pulse if it is to include ten cycles of the ultrasonic wave? (c) What is the spatial length of such a pulse?arrow_forward(a) Ear trumpets were never very common, but they did aid people with hearing losses by gathering sound over a large area and concentrating it on the smaller area of the eardrum. What decibel increase does an ear trumpet produce it its sound gathering area is 900 cm2 and the area of the eardrum is 0.500 cm2, but the trumpet only has an eficiency of 5.00% in transmitting the sound to the eardrum? (b) Comment on the usefulness of the decibel increase found in part (a).arrow_forwardHow do sound vibrations of atoms differ from thermal motion?arrow_forward
- In Section 16.7, we derived the speed of sound in a gas using the impulsemomentum theorem applied to the cylinder of gas in Figure 16.20. Let us find the speed of sound in a gas using a different approach based on the element of gas in Figure 16.18. Proceed as follows. (a) Draw a force diagram for this element showing the forces exerted on the left and right surfaces due to the pressure of the gas on either side of the element. (b) By applying Newtons second law to the element, show that (P)xAx=Ax2st2 (c) By substituting P = (B s/x) (Eq. 16.30), derive the following wave equation for sound: B2sx2=2st2 (d) To a mathematical physicist, this equation demonstrates the existence of sound waves and determines their speed. As a physics student, you must take another step or two. Substitute into the wave equation the trial solution s(x, t) = smax cos (kx t). Show that this function satisfies the wave equation, provided /k=v=B/.arrow_forwardAn interstate highway has been built through a neighborhood in a city. In the afternoon, the sound level in an apartment in the neighborhood is 80.0 dB as 100 cars pass outside the window every minute. Late at night, the traffic flow is only five cars per minute. What is the average late-night sound level?arrow_forwardEver since seeing Figure 16.22 in the previous chapter, you have been fascinated with the hearing response in humans. You have set up an apparatus that allows you to determine your own threshold of hearing as a function of frequency. After performing the experiment and recording the results, you graph the results, which look like Figure P17.22. You are intrigued by the two dips in the curve at the right-hand side of the graph. You measure carefully and find that the minimum values of these dips occur at 3 800 Hz and 11 500 Hz. Performing some online research, you discover that the outer canal of the human ear can be modeled as an air column open at the outer end and closed at the inner end by the eardrum. You use this information to determine the length of the outer canal in your car. Figure P17.22arrow_forward
- Review. An aluminum wire is held between two clamps under zero tension at room temperature. Reducing the temperature, which results in a decrease in the wires equilibrium length, increases the tension in the wire. Taking the cross-sectional area of the wire to be 5.00 10-6 m2, the density to be 2.70 103 kg/m3, and Young's modulus to be 7.00 1010 N/m2, what strain (L/L.) results in a transverse wave speed of 100 m/s?arrow_forwardAn aluminum rod is clamped one-fourth of the way along its length and set into longitudinal vibration by a variable-frequency driving source. The lowest frequency that produces resonance is 4 400 Hz. The speed of sound in an aluminum rod is 5 100 m/s. Determine the length of the rod.arrow_forwardAn astronomer measures the speed of recession of a remote galaxy to be 365 km/s using the Doppler principle According to the Hubble relation, about how far away is the galaxy?arrow_forward
- As a certain sound wave travels through the air, it produces pressure variations (above anti below atmospheric pressure) given by P = 1.27 sin (x - 34t) in SI units. Find (a) the amplitude of the pressure variations. (b) the frequency, (c) the wavelength in air. and (d| the speed of the sound wave.arrow_forwardYou are working for a plumber who is laying very long sections of copper pipe for a large building project. He spends a lot of time measuring the lengths of the sections with a measuring tape. You suggest a faster way to measure the length. You know that the speed of a one-dimensional compressional wave traveling along a copper pipe is 3.56 km/s. You suggest that a worker give a sharp hammer blow at one end of the pipe. Using an oscilloscope app on your smartphone, you will measure the time interval t between the arrival of the two sound waves due to the blow: one through the 20.0C air and the other through the pipe. (a) To measure the length, you must derive an equation that relates the length L of the pipe numerically to the time interval t. (b) You measure a time interval of t = 127 ms between the arrivals of the pulses and, from this value, determine the length of the pipe. (c) Your smartphone app claims an accuracy of 1.0% in measuring time intervals. So you calculate by how many centimeters your calculation of the length might be in error.arrow_forwardWrite an expression that describes the pressure variation as a function of position and time for a sinusoidal sound wave in air. Assume the speed of sound is 343 m/s, = 0.100 m, and Pmax = 0.200 Pa.arrow_forward
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